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What is the Least Common Multiple of 12 and 21?

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 12 and 21 is 84.

LCM(12,21) = 84

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Least Common Multiple of 12 and 21 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 12 and 21, than apply into the LCM equation.

GCF(12,21) = 3
LCM(12,21) = ( 12 × 21) / 3
LCM(12,21) = 252 / 3
LCM(12,21) = 84

Least Common Multiple (LCM) of 12 and 21 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 12 and 21. First we will calculate the prime factors of 12 and 21.

Prime Factorization of 12

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

12 = 22 × 31

Prime Factorization of 21

Prime factors of 21 are 3, 7. Prime factorization of 21 in exponential form is:

21 = 31 × 71

Now multiplying the highest exponent prime factors to calculate the LCM of 12 and 21.

LCM(12,21) = 22 × 31 × 71
LCM(12,21) = 84

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