Question
The LCM of 28, 60, 120 and 135
is:ÂSolution
Prime factorization 28 = 2 * 2 * 7 = 22 * 7 60 = 2 * 2 * 3 * 5 = 22 * 3 * 5 120 = 2 * 2 * 2 * 3 * 5 = 23 * 3 * 5 135 = 3 * 3 * 3 * 5 = 33 * 5 Take highest powers of all primes that appear Prime 2: max power is 23 (from 120) Prime 3: max power is 33 (from 135) Prime 5: max power is 51 Prime 7: max power is 71 So, LCM = 23 * 33 * 5 * 7 Multiply 23 = 8 33 = 27 8 * 27 = 216 216 * 5 = 1080 1080 * 7 = 7560 Therefore, LCM(28, 60, 120, 135) = 7560
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