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What is the Least Common Multiple of 77265 and 77280?

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 77265 and 77280 is 398069280.

LCM(77265,77280) = 398069280

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Least Common Multiple of 77265 and 77280 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 77265 and 77280, than apply into the LCM equation.

GCF(77265,77280) = 15
LCM(77265,77280) = ( 77265 × 77280) / 15
LCM(77265,77280) = 5971039200 / 15
LCM(77265,77280) = 398069280

Least Common Multiple (LCM) of 77265 and 77280 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 77265 and 77280. First we will calculate the prime factors of 77265 and 77280.

Prime Factorization of 77265

Prime factors of 77265 are 3, 5, 17, 101. Prime factorization of 77265 in exponential form is:

77265 = 32 × 51 × 171 × 1011

Prime Factorization of 77280

Prime factors of 77280 are 2, 3, 5, 7, 23. Prime factorization of 77280 in exponential form is:

77280 = 25 × 31 × 51 × 71 × 231

Now multiplying the highest exponent prime factors to calculate the LCM of 77265 and 77280.

LCM(77265,77280) = 32 × 51 × 171 × 1011 × 25 × 71 × 231
LCM(77265,77280) = 398069280