What is the Least Common Multiple of 420 and 427?
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 427 is 25620.
LCM(420,427) = 25620
Least Common Multiple of 420 and 427 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 427, than apply into the LCM equation.
GCF(420,427) = 7
LCM(420,427) = ( 420 × 427) / 7
LCM(420,427) = 179340 / 7
LCM(420,427) = 25620
Least Common Multiple (LCM) of 420 and 427 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 420 and 427. First we will calculate the prime factors of 420 and 427.
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 427
Prime factors of 427 are 7, 61. Prime factorization of 427 in exponential form is:
427 = 71 × 611
Now multiplying the highest exponent prime factors to calculate the LCM of 420 and 427.
LCM(420,427) = 22 × 31 × 51 × 71 × 611
LCM(420,427) = 25620
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