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Least Common Multiple of 15 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 15 and 21 is 105.

LCM(15,21) = 105

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Least Common Multiple of 15 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 15 and 21, than apply into the LCM equation.

GCF(15,21) = 3
LCM(15,21) = ( 15 × 21) / 3
LCM(15,21) = 315 / 3
LCM(15,21) = 105

Least Common Multiple (LCM) of 15 and 21 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 15 and 21. First we will calculate the prime factors of 15 and 21.

Prime Factorization of 15

Prime factors of 15 are 3, 5. Prime factorization of 15 in exponential form is:

15 = 31 × 51

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 15 and 21.

LCM(15,21) = 31 × 51 × 71
LCM(15,21) = 105

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