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What is the Least Common Multiple of 7200 and 7204?

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 7200 and 7204 is 12967200.

LCM(7200,7204) = 12967200

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Least Common Multiple of 7200 and 7204 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 7200 and 7204, than apply into the LCM equation.

GCF(7200,7204) = 4
LCM(7200,7204) = ( 7200 × 7204) / 4
LCM(7200,7204) = 51868800 / 4
LCM(7200,7204) = 12967200

Least Common Multiple (LCM) of 7200 and 7204 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 7200 and 7204. First we will calculate the prime factors of 7200 and 7204.

Prime Factorization of 7200

Prime factors of 7200 are 2, 3, 5. Prime factorization of 7200 in exponential form is:

7200 = 25 × 32 × 52

Prime Factorization of 7204

Prime factors of 7204 are 2, 1801. Prime factorization of 7204 in exponential form is:

7204 = 22 × 18011

Now multiplying the highest exponent prime factors to calculate the LCM of 7200 and 7204.

LCM(7200,7204) = 25 × 32 × 52 × 18011
LCM(7200,7204) = 12967200