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What is the Least Common Multiple of 49968 and 49984?

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 49968 and 49984 is 156100032.

LCM(49968,49984) = 156100032

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Least Common Multiple of 49968 and 49984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 49968 and 49984, than apply into the LCM equation.

GCF(49968,49984) = 16
LCM(49968,49984) = ( 49968 × 49984) / 16
LCM(49968,49984) = 2497600512 / 16
LCM(49968,49984) = 156100032

Least Common Multiple (LCM) of 49968 and 49984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 49968 and 49984. First we will calculate the prime factors of 49968 and 49984.

Prime Factorization of 49968

Prime factors of 49968 are 2, 3, 347. Prime factorization of 49968 in exponential form is:

49968 = 24 × 32 × 3471

Prime Factorization of 49984

Prime factors of 49984 are 2, 11, 71. Prime factorization of 49984 in exponential form is:

49984 = 26 × 111 × 711

Now multiplying the highest exponent prime factors to calculate the LCM of 49968 and 49984.

LCM(49968,49984) = 26 × 32 × 3471 × 111 × 711
LCM(49968,49984) = 156100032