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What is the Least Common Multiple of 30408 and 30416?

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 30408 and 30416 is 115611216.

LCM(30408,30416) = 115611216

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Least Common Multiple of 30408 and 30416 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30408 and 30416, than apply into the LCM equation.

GCF(30408,30416) = 8
LCM(30408,30416) = ( 30408 × 30416) / 8
LCM(30408,30416) = 924889728 / 8
LCM(30408,30416) = 115611216

Least Common Multiple (LCM) of 30408 and 30416 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30408 and 30416. First we will calculate the prime factors of 30408 and 30416.

Prime Factorization of 30408

Prime factors of 30408 are 2, 3, 7, 181. Prime factorization of 30408 in exponential form is:

30408 = 23 × 31 × 71 × 1811

Prime Factorization of 30416

Prime factors of 30416 are 2, 1901. Prime factorization of 30416 in exponential form is:

30416 = 24 × 19011

Now multiplying the highest exponent prime factors to calculate the LCM of 30408 and 30416.

LCM(30408,30416) = 24 × 31 × 71 × 1811 × 19011
LCM(30408,30416) = 115611216