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What is the Least Common Multiple of 54950 and 54960?

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 54950 and 54960 is 302005200.

LCM(54950,54960) = 302005200

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Least Common Multiple of 54950 and 54960 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54950 and 54960, than apply into the LCM equation.

GCF(54950,54960) = 10
LCM(54950,54960) = ( 54950 × 54960) / 10
LCM(54950,54960) = 3020052000 / 10
LCM(54950,54960) = 302005200

Least Common Multiple (LCM) of 54950 and 54960 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54950 and 54960. First we will calculate the prime factors of 54950 and 54960.

Prime Factorization of 54950

Prime factors of 54950 are 2, 5, 7, 157. Prime factorization of 54950 in exponential form is:

54950 = 21 × 52 × 71 × 1571

Prime Factorization of 54960

Prime factors of 54960 are 2, 3, 5, 229. Prime factorization of 54960 in exponential form is:

54960 = 24 × 31 × 51 × 2291

Now multiplying the highest exponent prime factors to calculate the LCM of 54950 and 54960.

LCM(54950,54960) = 24 × 52 × 71 × 1571 × 31 × 2291
LCM(54950,54960) = 302005200