What is the Least Common Multiple of 428 and 448?
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 428 and 448 is 47936.
LCM(428,448) = 47936
Least Common Multiple of 428 and 448 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 428 and 448, than apply into the LCM equation.
GCF(428,448) = 4
LCM(428,448) = ( 428 × 448) / 4
LCM(428,448) = 191744 / 4
LCM(428,448) = 47936
Least Common Multiple (LCM) of 428 and 448 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 428 and 448. First we will calculate the prime factors of 428 and 448.
Prime Factorization of 428
Prime factors of 428 are 2, 107. Prime factorization of 428 in exponential form is:
428 = 22 × 1071
Prime Factorization of 448
Prime factors of 448 are 2, 7. Prime factorization of 448 in exponential form is:
448 = 26 × 71
Now multiplying the highest exponent prime factors to calculate the LCM of 428 and 448.
LCM(428,448) = 26 × 1071 × 71
LCM(428,448) = 47936
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