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What is the Least Common Multiple of 73704 and 73720?

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 73704 and 73720 is 679182360.

LCM(73704,73720) = 679182360

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Least Common Multiple of 73704 and 73720 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 73704 and 73720, than apply into the LCM equation.

GCF(73704,73720) = 8
LCM(73704,73720) = ( 73704 × 73720) / 8
LCM(73704,73720) = 5433458880 / 8
LCM(73704,73720) = 679182360

Least Common Multiple (LCM) of 73704 and 73720 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 73704 and 73720. First we will calculate the prime factors of 73704 and 73720.

Prime Factorization of 73704

Prime factors of 73704 are 2, 3, 37, 83. Prime factorization of 73704 in exponential form is:

73704 = 23 × 31 × 371 × 831

Prime Factorization of 73720

Prime factors of 73720 are 2, 5, 19, 97. Prime factorization of 73720 in exponential form is:

73720 = 23 × 51 × 191 × 971

Now multiplying the highest exponent prime factors to calculate the LCM of 73704 and 73720.

LCM(73704,73720) = 23 × 31 × 371 × 831 × 51 × 191 × 971
LCM(73704,73720) = 679182360