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3x-520 = -517
Marvin Schuster
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What is the LCM of 15 20 and 8?
The LCM (least common multiple) of 8,15, and 20 is 120. Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, ... Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, ... Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, ... The number in each list that is the least is 120. Another way to calculate the LCM is to prime factorize: 8: 2 x 2 x 2 15: 3 x 5 20: 2 x 2 x 5 Now we must have the values for each included. So for 8 we know we need at least three 2s so we'll add them. Now we have 2 x 2 x 2. We need at least a 3 and a 5 for 15 which we don't have yet so we'll add them both. Now we have 2 x 2 x 2 x 3 x 5. For 20 we need at least two 2s and a 5 both of which we already included so we don't need to add anything else. So we have 2 x 2 x 2 x 3 x 5 = 120 Another method to do this is to realize that 8 and 15 are relatively prime (meaning they have no commons factors other than 1). This means the LCM of 8 and 15 is their product, 120. Because this number is also divisible by 20, it is the LCM of 8, 15, and 20. The LCM of 8, 15, and 20 is 120.Proof. Represent all numbers as products of prime factors8=2315=3x520=2x2x5The LCM should contain all these primes raised to the maximum power occurring above:LCM=23x3x5=120A: Some what simpler, 8 and 15 are relatively prime (no common factors), so their least common multiple is their product (which is 120). Since 120 is divisible by 20, it is also the LCM of the three numbers collectively.
