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What is the Least Common Multiple of 13974 and 13989?

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 13974 and 13989 is 65160762.

LCM(13974,13989) = 65160762

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Least Common Multiple of 13974 and 13989 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13974 and 13989, than apply into the LCM equation.

GCF(13974,13989) = 3
LCM(13974,13989) = ( 13974 × 13989) / 3
LCM(13974,13989) = 195482286 / 3
LCM(13974,13989) = 65160762

Least Common Multiple (LCM) of 13974 and 13989 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13974 and 13989. First we will calculate the prime factors of 13974 and 13989.

Prime Factorization of 13974

Prime factors of 13974 are 2, 3, 17, 137. Prime factorization of 13974 in exponential form is:

13974 = 21 × 31 × 171 × 1371

Prime Factorization of 13989

Prime factors of 13989 are 3, 4663. Prime factorization of 13989 in exponential form is:

13989 = 31 × 46631

Now multiplying the highest exponent prime factors to calculate the LCM of 13974 and 13989.

LCM(13974,13989) = 21 × 31 × 171 × 1371 × 46631
LCM(13974,13989) = 65160762