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What is the Least Common Multiple of 54750 and 54762?

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 54750 and 54762 is 499703250.

LCM(54750,54762) = 499703250

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Least Common Multiple of 54750 and 54762 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54750 and 54762, than apply into the LCM equation.

GCF(54750,54762) = 6
LCM(54750,54762) = ( 54750 × 54762) / 6
LCM(54750,54762) = 2998219500 / 6
LCM(54750,54762) = 499703250

Least Common Multiple (LCM) of 54750 and 54762 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54750 and 54762. First we will calculate the prime factors of 54750 and 54762.

Prime Factorization of 54750

Prime factors of 54750 are 2, 3, 5, 73. Prime factorization of 54750 in exponential form is:

54750 = 21 × 31 × 53 × 731

Prime Factorization of 54762

Prime factors of 54762 are 2, 3, 9127. Prime factorization of 54762 in exponential form is:

54762 = 21 × 31 × 91271

Now multiplying the highest exponent prime factors to calculate the LCM of 54750 and 54762.

LCM(54750,54762) = 21 × 31 × 53 × 731 × 91271
LCM(54750,54762) = 499703250