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What is the Least Common Multiple of 54969 and 54984?

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 54969 and 54984 is 1007471832.

LCM(54969,54984) = 1007471832

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Least Common Multiple of 54969 and 54984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 54969 and 54984, than apply into the LCM equation.

GCF(54969,54984) = 3
LCM(54969,54984) = ( 54969 × 54984) / 3
LCM(54969,54984) = 3022415496 / 3
LCM(54969,54984) = 1007471832

Least Common Multiple (LCM) of 54969 and 54984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 54969 and 54984. First we will calculate the prime factors of 54969 and 54984.

Prime Factorization of 54969

Prime factors of 54969 are 3, 73, 251. Prime factorization of 54969 in exponential form is:

54969 = 31 × 731 × 2511

Prime Factorization of 54984

Prime factors of 54984 are 2, 3, 29, 79. Prime factorization of 54984 in exponential form is:

54984 = 23 × 31 × 291 × 791

Now multiplying the highest exponent prime factors to calculate the LCM of 54969 and 54984.

LCM(54969,54984) = 31 × 731 × 2511 × 23 × 291 × 791
LCM(54969,54984) = 1007471832