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What is the Least Common Multiple of 2700 and 2720?

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 2700 and 2720 is 367200.

LCM(2700,2720) = 367200

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Least Common Multiple of 2700 and 2720 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 2700 and 2720, than apply into the LCM equation.

GCF(2700,2720) = 20
LCM(2700,2720) = ( 2700 × 2720) / 20
LCM(2700,2720) = 7344000 / 20
LCM(2700,2720) = 367200

Least Common Multiple (LCM) of 2700 and 2720 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 2700 and 2720. First we will calculate the prime factors of 2700 and 2720.

Prime Factorization of 2700

Prime factors of 2700 are 2, 3, 5. Prime factorization of 2700 in exponential form is:

2700 = 22 × 33 × 52

Prime Factorization of 2720

Prime factors of 2720 are 2, 5, 17. Prime factorization of 2720 in exponential form is:

2720 = 25 × 51 × 171

Now multiplying the highest exponent prime factors to calculate the LCM of 2700 and 2720.

LCM(2700,2720) = 25 × 33 × 52 × 171
LCM(2700,2720) = 367200