# What is the Least Common Multiple of 8 and 10?

*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 = 2^{3}

### Prime Factorization of 10

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

10 = 2^{1} × 5^{1}

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

LCM(8,10) = 2^{3} × 5^{1}

LCM(8,10) = 40

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