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Least Common Multiple of 4 and 10

Free LCM Calculator determines the least common multiple (LCM) between 4 and 10 the smallest integer that is 20 that is divisible by both numbers.

Least Common Multiple (LCM) of 4 and 10 is 20.

LCM(4,10) = 20

LCM of 4 and 10

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

LCM of:
and

Least Common Multiple (LCM) of 4 and 10 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 4 and 10. First we will calculate the prime factors of 4 and 10.

Prime Factorization of 4


2 4
2 2
1

Prime factors of 4 are 2. Prime factorization of 4 in exponential form is:

4 = 22

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 4 and 10.

LCM(4,10) = 22×51
LCM(4,10) = 20

Factors of 4

List of positive integer factors of 4 that divides 4 without a remainder.

1, 2, 4

Factors of 10

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

1, 2, 5, 10

Least Common Multiple of 4 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 4 and 10, than apply into the LCM equation.

GCF(4,10) = 2
LCM(4,10) = ( 4 × 10) / 2
LCM(4,10) = 40 / 2
LCM(4,10) = 20

Least Common Multiple of 4 and 10 by Listing Multiples

Multiples of 4

4, 8, 12, 16,20

Multiples of 10

10,20

Find the smallest number that is on all of the lists. We have it in bold above.

∴ Least Common Multiple of 4 and 10 is 20

Properties of LCM 4 and 10

(i) The LCM of 10 and 4 is associative

LCM of 4 and 10 = LCM of 10 and 4

Frequently Asked Questions on LCM of 4 and 10

1. What is the LCM of 4 and 10?

Answer: LCM of 4 and 10 is 20.

2. What are the Factors of 4?

Answer: Factors of 4 are 1, 2, 4. There are 3 integers that are factors of 4. The greatest factor of 4 is 4.

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 4 and 10?

Answer:

Least Common Multiple of 4 and 10 = 20

Step 1: Find the prime factorization of 4

4 = 2 x 2

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 = 20 = 2 x 2 x 5

Step 4: Therefore, the least common multiple of 4 and 10 is 20.