What is the Least Common Multiple of 420 and 428?
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 420 and 428 is 44940.
LCM(420,428) = 44940
Least Common Multiple of 420 and 428 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 420 and 428, than apply into the LCM equation.
GCF(420,428) = 4
LCM(420,428) = ( 420 × 428) / 4
LCM(420,428) = 179760 / 4
LCM(420,428) = 44940
Least Common Multiple (LCM) of 420 and 428 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 420 and 428. First we will calculate the prime factors of 420 and 428.
Prime Factorization of 420
Prime factors of 420 are 2, 3, 5, 7. Prime factorization of 420 in exponential form is:
420 = 22 × 31 × 51 × 71
Prime Factorization of 428
Prime factors of 428 are 2, 107. Prime factorization of 428 in exponential form is:
428 = 22 × 1071
Now multiplying the highest exponent prime factors to calculate the LCM of 420 and 428.
LCM(420,428) = 22 × 31 × 51 × 71 × 1071
LCM(420,428) = 44940
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