Least Common Multiple of 10 and 28

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 10 and 28 the smallest integer that is 140 that is divisible by both numbers.

Least Common Multiple (LCM) of 10 and 28 is 140.

LCM(10,28) = 140

LCM of 10 and 28

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

LCM of:
and

Least Common Multiple of 10 and 28

LCM of 10 and 28 is 140

Least common multiple can be found by multiplying the highest exponent prime factors of 10 and 28. First we will calculate the prime factors of 10 and 28.

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

Prime Factorization of 28


2 28
2 14
7 7
1

Prime factors of 28 are 2,7. Prime factorization of 28 in exponential form is:

28 = 22×71

Now multiplying the highest exponent prime factors to calculate the LCM of 10 and 28.

LCM(10,28) = 22×51×71
LCM(10,28) = 140

Factors of 10

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

1, 2, 5, 10

Factors of 28

List of positive integer factors of 28 that divides 28 without a remainder.

1, 2, 4, 7, 14, 28

Least Common Multiple of 10 and 28 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 10 and 28, than apply into the LCM equation.

GCF(10,28) = 2
LCM(10,28) = ( 10 × 28) / 2
LCM(10,28) = 280 / 2
LCM(10,28) = 140

Properties of LCM 10 and 28

(i) The LCM of 28 and 10 is associative

LCM of 10 and 28 = LCM of 28 and 10

Related Least Common Multiples of 10

Related Least Common Multiples of 28

Frequently Asked Questions on LCM of 10 and 28

1. What is the LCM of 10 and 28?

Answer: LCM of 10 and 28 is 140.

2. 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.

3. What are the Factors of 28?

Answer: Factors of 28 are 1, 2, 4, 7, 14, 28. There are 6 integers that are factors of 28. The greatest factor of 28 is 28.

4. How to Find the LCM of 10 and 28?

Answer:

Least Common Multiple of 10 and 28 = 140

Step 1: Find the prime factorization of 10

10 = 2 x 5

Step 2: Find the prime factorization of 28

28 = 2 x 2 x 7

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

LCM = 140 = 2 x 2 x 5 x 7

Step 4: Therefore, the least common multiple of 10 and 28 is 140.