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What is the Least Common Multiple of 10 and 12?

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 10 and 12 is 60.

LCM(10,12) = 60

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Least Common Multiple of 10 and 12 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 12, than apply into the LCM equation.

GCF(10,12) = 2
LCM(10,12) = ( 10 × 12) / 2
LCM(10,12) = 120 / 2
LCM(10,12) = 60

Least Common Multiple (LCM) of 10 and 12 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 10 and 12. First we will calculate the prime factors of 10 and 12.

Prime Factorization of 10

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

10 = 21 × 51

Prime Factorization of 12

Prime factors of 12 are 2, 3. Prime factorization of 12 in exponential form is:

12 = 22 × 31

Now multiplying the highest exponent prime factors to calculate the LCM of 10 and 12.

LCM(10,12) = 22 × 51 × 31
LCM(10,12) = 60

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