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What is the Least Common Multiple of 29968 and 29984?

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 29968 and 29984 is 56160032.

LCM(29968,29984) = 56160032

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Least Common Multiple of 29968 and 29984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 29968 and 29984, than apply into the LCM equation.

GCF(29968,29984) = 16
LCM(29968,29984) = ( 29968 × 29984) / 16
LCM(29968,29984) = 898560512 / 16
LCM(29968,29984) = 56160032

Least Common Multiple (LCM) of 29968 and 29984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 29968 and 29984. First we will calculate the prime factors of 29968 and 29984.

Prime Factorization of 29968

Prime factors of 29968 are 2, 1873. Prime factorization of 29968 in exponential form is:

29968 = 24 × 18731

Prime Factorization of 29984

Prime factors of 29984 are 2, 937. Prime factorization of 29984 in exponential form is:

29984 = 25 × 9371

Now multiplying the highest exponent prime factors to calculate the LCM of 29968 and 29984.

LCM(29968,29984) = 25 × 18731 × 9371
LCM(29968,29984) = 56160032