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What is the Least Common Multiple of 30162 and 30170?

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 30162 and 30170 is 454993770.

LCM(30162,30170) = 454993770

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Least Common Multiple of 30162 and 30170 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30162 and 30170, than apply into the LCM equation.

GCF(30162,30170) = 2
LCM(30162,30170) = ( 30162 × 30170) / 2
LCM(30162,30170) = 909987540 / 2
LCM(30162,30170) = 454993770

Least Common Multiple (LCM) of 30162 and 30170 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30162 and 30170. First we will calculate the prime factors of 30162 and 30170.

Prime Factorization of 30162

Prime factors of 30162 are 2, 3, 11, 457. Prime factorization of 30162 in exponential form is:

30162 = 21 × 31 × 111 × 4571

Prime Factorization of 30170

Prime factors of 30170 are 2, 5, 7, 431. Prime factorization of 30170 in exponential form is:

30170 = 21 × 51 × 71 × 4311

Now multiplying the highest exponent prime factors to calculate the LCM of 30162 and 30170.

LCM(30162,30170) = 21 × 31 × 111 × 4571 × 51 × 71 × 4311
LCM(30162,30170) = 454993770