What is the Least Common Multiple of 408 and 412?
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 408 and 412 is 42024.
LCM(408,412) = 42024
Least Common Multiple of 408 and 412 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 408 and 412, than apply into the LCM equation.
GCF(408,412) = 4
LCM(408,412) = ( 408 × 412) / 4
LCM(408,412) = 168096 / 4
LCM(408,412) = 42024
Least Common Multiple (LCM) of 408 and 412 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 408 and 412. First we will calculate the prime factors of 408 and 412.
Prime Factorization of 408
Prime factors of 408 are 2, 3, 17. Prime factorization of 408 in exponential form is:
408 = 23 × 31 × 171
Prime Factorization of 412
Prime factors of 412 are 2, 103. Prime factorization of 412 in exponential form is:
412 = 22 × 1031
Now multiplying the highest exponent prime factors to calculate the LCM of 408 and 412.
LCM(408,412) = 23 × 31 × 171 × 1031
LCM(408,412) = 42024
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