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Least Common Multiple of 30 and 42

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 30 and 42 is 210.

LCM(30,42) = 210

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Least Common Multiple of 30 and 42 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 30 and 42, than apply into the LCM equation.

GCF(30,42) = 6
LCM(30,42) = ( 30 × 42) / 6
LCM(30,42) = 1260 / 6
LCM(30,42) = 210

Least Common Multiple (LCM) of 30 and 42 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 30 and 42. First we will calculate the prime factors of 30 and 42.

Prime Factorization of 30

Prime factors of 30 are 2, 3, 5. Prime factorization of 30 in exponential form is:

30 = 21 × 31 × 51

Prime Factorization of 42

Prime factors of 42 are 2, 3, 7. Prime factorization of 42 in exponential form is:

42 = 21 × 31 × 71

Now multiplying the highest exponent prime factors to calculate the LCM of 30 and 42.

LCM(30,42) = 21 × 31 × 51 × 71
LCM(30,42) = 210

Recent Comments
asscia stewart 2019-10-03 17:17:50

i like this math it helps me with my home work.

Kim Taehyung 2018-10-28 15:50:46

Because its the least common factor doesnt matter just that they are for the same factors for both numbers

ashiq 2018-09-20 21:40:19

i am confused because 6 is also the factor of 42 i mean 42 can also be divided by 6 then the lcm of 42 should be 2,3,6,7. but 6 not counted as prime factor why .

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