Least Common Multiple of 56 and 10

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 56 and 10 the smallest integer that is 280 that is divisible by both numbers.

Least Common Multiple (LCM) of 56 and 10 is 280.

LCM(56,10) = 280

LCM of 56 and 10

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 56 and 10

LCM of 56 and 10 is 280

Least common multiple can be found by multiplying the highest exponent prime factors of 56 and 10. First we will calculate the prime factors of 56 and 10.

Prime Factorization of 56


2 56
2 28
2 14
7 7
1

Prime factors of 56 are 2,7. Prime factorization of 56 in exponential form is:

56 = 23×71

Prime Factorization of 10


2 10
5 5
1

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 56 and 10.

LCM(56,10) = 23×51×71
LCM(56,10) = 280

Factors of 56

List of positive integer factors of 56 that divides 56 without a remainder.

1, 2, 4, 7, 8, 14, 28, 56

Factors of 10

List of positive integer factors of 10 that divides 10 without a remainder.

1, 2, 5, 10

Least Common Multiple of 56 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 56 and 10, than apply into the LCM equation.

GCF(56,10) = 2
LCM(56,10) = ( 56 × 10) / 2
LCM(56,10) = 560 / 2
LCM(56,10) = 280

Properties of LCM 56 and 10

(i) The LCM of 10 and 56 is associative

LCM of 56 and 10 = LCM of 10 and 56

Related Least Common Multiples of 56

Related Least Common Multiples of 10

Frequently Asked Questions on LCM of 56 and 10

1. What is the LCM of 56 and 10?

Answer: LCM of 56 and 10 is 280.

2. What are the Factors of 56?

Answer: Factors of 56 are 1, 2, 4, 7, 8, 14, 28, 56. There are 8 integers that are factors of 56. The greatest factor of 56 is 56.

3. What are the Factors of 10?

Answer: Factors of 10 are 1, 2, 5, 10. There are 4 integers that are factors of 10. The greatest factor of 10 is 10.

4. How to Find the LCM of 56 and 10?

Answer:

Least Common Multiple of 56 and 10 = 280

Step 1: Find the prime factorization of 56

56 = 2 x 2 x 2 x 7

Step 2: Find the prime factorization of 10

10 = 2 x 5

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 280 = 2 x 2 x 2 x 5 x 7

Step 4: Therefore, the least common multiple of 56 and 10 is 280.