What is the lcm for 8 and 10

LCM of 8, 10 and 16 is equal to 80. The comprehensive work provides more insight of how to find what is the lcm of 8, 10 and 16 by using prime factors and special division methods, and the example use case of mathematics and real world problems.

Índice Show

Least Common Multiple of 8 and 10 with GCF Formula
Least Common Multiple (LCM) of 8 and 10 with Primes
Prime Factorization of 8
Prime Factorization of 10
What is the LCM of 8 and 10?
Methods to Find LCM of 8 and 10
LCM of 8 and 10 by Prime Factorization
LCM of 8 and 10 by Listing Multiples
LCM of 8 and 10 by Division Method
What is the Relation Between GCF and LCM of 8, 10?
If the LCM of 10 and 8 is 40, Find its GCF.
What is the Least Perfect Square Divisible by 8 and 10?
Which of the following is the LCM of 8 and 10? 36, 40, 35, 3

what is the lcm of 8, 10 and 16?

lcm (8 10 16) = (?) 8 => 2 x 2 x 2 10 => 2 x 5 16 => 2 x 2 x 2 x 2

= 2 x 2 x 2 x 5 x 2

= 80 lcm (8, 10 and 16) = 80

80 is the lcm of 8, 10 and 16.

where,

8 is a positive integer, 10 is a positive integer, 80 is the lcm of 8, 10 and 16,

{2, 2, 2} in {2 x 2 x 2, 2 x 5, 2 x 2 x 2 x 2} are the most repeated factors of 8, 10 and 16,

{5, 2} in {2 x 2 x 2, 2 x 5, 2 x 2 x 2 x 2} are the the other remaining factors of 8, 10 and 16.

Use in Mathematics: LCM of 8, 10 and 16

The below are some of the mathematical applications where lcm of 8, 10 and 16 can be used:

to find the least number which is exactly divisible by 8, 10 and 16.
to find the common denominators for the fractions having 8, 10 and 16 as denominators in the unlike fractions addition or subtraction.

Use in Real-world Problems: 8, 10 and 16 lcm In the context of lcm real world problems, the lcm of 8, 10 and 16 helps to find the exact time when three similar and recurring with different time schedule happens together at the same time. For example, the real world problems involve lcm in situations to find at what time all the bells A, B and C toll together, if bell A tolls at 8 seconds, B tolls at 10 seconds and C tolls at 16 seconds repeatedly. The answer is that all bells A, B and C toll together at 80 seconds for the first time, at 160 seconds for the second time, at 240 seconds for the third time and so on.

Important Notes: 8, 10 and 16 lcm

The below are the important notes to be remembered while solving the lcm of 8, 10 and 16:

The repeated and non-repeated prime factors of 8, 10 and 16 should be multiplied to find the least common multiple of 8, 10 and 16, when solving lcm by using prime factors method.
The results of lcm of 8, 10 and 16 is identical even if we change the order of given numbers in the lcm calculation, it means the order of given numbers in the lcm calculation doesn't affect the results.

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 8 and 10 is 40.

LCM(8,10) = 40

Least Common Multiple of 8 and 10 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 8 and 10, than apply into the LCM equation.

GCF(8,10) = 2 LCM(8,10) = ( 8 × 10) / 2 LCM(8,10) = 80 / 2

LCM(8,10) = 40

Least Common Multiple (LCM) of 8 and 10 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 8 and 10. First we will calculate the prime factors of 8 and 10.

Prime Factorization of 8

Prime factors of 8 are 2. Prime factorization of 8 in exponential form is:

8 = 23

Prime Factorization of 10

Prime factors of 10 are 2, 5. Prime factorization of 10 in exponential form is:

10 = 21 × 51

Now multiplying the highest exponent prime factors to calculate the LCM of 8 and 10.

LCM(8,10) = 23 × 51
LCM(8,10) = 40

The LCM of 8 and 10 is 40.

Steps to find LCM

Find the prime factorization of 8
8 = 2 × 2 × 2
Find the prime factorization of 10
10 = 2 × 5
Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:
LCM = 2 × 2 × 2 × 5
LCM = 40

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Find least common multiple (LCM) of: 16 & 20 4 & 5 24 & 30 40 & 50 56 & 70 16 & 10 8 & 20 24 & 10 8 & 30 40 & 10 8 & 50 56 & 10 8 & 70

Enter two numbers separate by comma. To find least common multiple (LCM) of more than two numbers, click here.

LCM of 8 and 10 is the smallest number among all common multiples of 8 and 10. The first few multiples of 8 and 10 are (8, 16, 24, 32, 40, . . . ) and (10, 20, 30, 40, . . . ) respectively. There are 3 commonly used methods to find LCM of 8 and 10 - by prime factorization, by listing multiples, and by division method.

What is the LCM of 8 and 10?

Answer: LCM of 8 and 10 is 40.

Explanation:

The LCM of two non-zero integers, x(8) and y(10), is the smallest positive integer m(40) that is divisible by both x(8) and y(10) without any remainder.

Methods to Find LCM of 8 and 10

Let's look at the different methods for finding the LCM of 8 and 10.

By Prime Factorization Method
By Listing Multiples
By Division Method

LCM of 8 and 10 by Prime Factorization

Prime factorization of 8 and 10 is (2 × 2 × 2) = 23 and (2 × 5) = 21 × 51 respectively. LCM of 8 and 10 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 23 × 51 = 40.
Hence, the LCM of 8 and 10 by prime factorization is 40.

LCM of 8 and 10 by Listing Multiples

To calculate the LCM of 8 and 10 by listing out the common multiples, we can follow the given below steps:

Step 1: List a few multiples of 8 (8, 16, 24, 32, 40, . . . ) and 10 (10, 20, 30, 40, . . . . )
Step 2: The common multiples from the multiples of 8 and 10 are 40, 80, . . .
Step 3: The smallest common multiple of 8 and 10 is 40.

∴ The least common multiple of 8 and 10 = 40.

LCM of 8 and 10 by Division Method

To calculate the LCM of 8 and 10 by the division method, we will divide the numbers(8, 10) by their prime factors (preferably common). The product of these divisors gives the LCM of 8 and 10.

Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 8 and 10. Write this prime number(2) on the left of the given numbers(8 and 10), separated as per the ladder arrangement.
Step 2: If any of the given numbers (8, 10) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.
Step 3: Continue the steps until only 1s are left in the last row.

The LCM of 8 and 10 is the product of all prime numbers on the left, i.e. LCM(8, 10) by division method = 2 × 2 × 2 × 5 = 40.

☛ Also Check:

Example 1: Verify the relationship between GCF and LCM of 8 and 10.

Solution:

The relation between GCF and LCM of 8 and 10 is given as, LCM(8, 10) × GCF(8, 10) = Product of 8, 10
Prime factorization of 8 and 10 is given as, 8 = (2 × 2 × 2) = 23 and 10 = (2 × 5) = 21 × 51
LCM(8, 10) = 40 GCF(8, 10) = 2 LHS = LCM(8, 10) × GCF(8, 10) = 40 × 2 = 80 RHS = Product of 8, 10 = 8 × 10 = 80 ⇒ LHS = RHS = 80
Hence, verified.

Example 2: The product of two numbers is 80. If their GCD is 2, what is their LCM?

Solution:

Given: GCD = 2 product of numbers = 80 ∵ LCM × GCD = product of numbers ⇒ LCM = Product/GCD = 80/2 Therefore, the LCM is 40.

The probable combination for the given case is LCM(8, 10) = 40.

Example 3: The GCD and LCM of two numbers are 2 and 40 respectively. If one number is 10, find the other number.

Solution:

Let the other number be a.
∵ GCD × LCM = 10 × a ⇒ a = (GCD × LCM)/10 ⇒ a = (2 × 40)/10 ⇒ a = 8

Therefore, the other number is 8.

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The LCM of 8 and 10 is 40. To find the least common multiple of 8 and 10, we need to find the multiples of 8 and 10 (multiples of 8 = 8, 16, 24, 32 . . . . 40; multiples of 10 = 10, 20, 30, 40) and choose the smallest multiple that is exactly divisible by 8 and 10, i.e., 40.

What is the Relation Between GCF and LCM of 8, 10?

The following equation can be used to express the relation between GCF and LCM of 8 and 10, i.e. GCF × LCM = 8 × 10.

If the LCM of 10 and 8 is 40, Find its GCF.

LCM(10, 8) × GCF(10, 8) = 10 × 8 Since the LCM of 10 and 8 = 40 ⇒ 40 × GCF(10, 8) = 80

Therefore, the greatest common factor (GCF) = 80/40 = 2.

What is the Least Perfect Square Divisible by 8 and 10?

The least number divisible by 8 and 10 = LCM(8, 10)
LCM of 8 and 10 = 2 × 2 × 2 × 5 [Incomplete pair(s): 2, 5]
⇒ Least perfect square divisible by each 8 and 10 = LCM(8, 10) × 2 × 5 = 400 [Square root of 400 = √400 = ±20]
Therefore, 400 is the required number.