least common multiple(lcm)
the smallest whole number greater than zero that is a common multiple of each of two or more multiples
The Least Common Multiple (LCM) is the smallest multiple that two or more numbers have in common. To find the LCM of two or more numbers, we need to list their multiples and find the smallest multiple that they have in common.
For example, let’s find the LCM of 4, 6, and 8:
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40…
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60…
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80…
We can see that the smallest multiple that all three numbers have in common is 24. Therefore, the LCM of 4, 6, and 8 is 24.
To find the LCM of larger numbers, we can use different methods such as prime factorization or the division method. Using prime factorization involves finding the prime factors of each number, multiplying the highest power of each prime factor together, and the resulting product is the LCM.
For example, let’s find the LCM of 12, 15, and 18 using prime factorization:
12 = 2^2 x 3
15 = 3 x 5
18 = 2 x 3^2
To find the LCM, we need to take the highest power of each prime factor and multiply them together:
2^2 x 3^2 x 5 = 180
Therefore, the LCM of 12, 15, and 18 is 180.
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