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What is the Least Common Multiple of 54945 and 54964?

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 54945 and 54964 is 3019996980.

LCM(54945,54964) = 3019996980

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Least Common Multiple of 54945 and 54964 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54945 and 54964, than apply into the LCM equation.

GCF(54945,54964) = 1
LCM(54945,54964) = ( 54945 × 54964) / 1
LCM(54945,54964) = 3019996980 / 1
LCM(54945,54964) = 3019996980

Least Common Multiple (LCM) of 54945 and 54964 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54945 and 54964. First we will calculate the prime factors of 54945 and 54964.

Prime Factorization of 54945

Prime factors of 54945 are 3, 5, 11, 37. Prime factorization of 54945 in exponential form is:

54945 = 33 × 51 × 111 × 371

Prime Factorization of 54964

Prime factors of 54964 are 2, 7, 13, 151. Prime factorization of 54964 in exponential form is:

54964 = 22 × 71 × 131 × 1511

Now multiplying the highest exponent prime factors to calculate the LCM of 54945 and 54964.

LCM(54945,54964) = 33 × 51 × 111 × 371 × 22 × 71 × 131 × 1511
LCM(54945,54964) = 3019996980