What is the Least Common Multiple of 378 and 398?
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 378 and 398 is 75222.
LCM(378,398) = 75222
Least Common Multiple of 378 and 398 with GCF Formula
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 378 and 398, than apply into the LCM equation.
GCF(378,398) = 2
LCM(378,398) = ( 378 × 398) / 2
LCM(378,398) = 150444 / 2
LCM(378,398) = 75222
Least Common Multiple (LCM) of 378 and 398 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 378 and 398. First we will calculate the prime factors of 378 and 398.
Prime Factorization of 378
Prime factors of 378 are 2, 3, 7. Prime factorization of 378 in exponential form is:
378 = 21 × 33 × 71
Prime Factorization of 398
Prime factors of 398 are 2, 199. Prime factorization of 398 in exponential form is:
398 = 21 × 1991
Now multiplying the highest exponent prime factors to calculate the LCM of 378 and 398.
LCM(378,398) = 21 × 33 × 71 × 1991
LCM(378,398) = 75222
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