What is the least common multiple LCM of 8 and 11?

The least common multiple (LCM) of 8 and 11 is 88.

The LCM is the smallest positive integer that is divisible by both numbers. Here's how to find it:

• Method 1: Listing Multiples

  • Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96...
  • Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99...

  The smallest multiple that appears in both lists is 88.

• Method 2: Prime Factorization

  • Prime factorization of 8: 2 x 2 x 2 = 2³
  • Prime factorization of 11: 11

  To find the LCM, take the highest power of each prime factor that appears in either factorization and multiply them together: 2³ x 11 = 8 x 11 = 88

• Method 3: Using the Formula

  LCM(a, b) = (|a * b|) / GCD(a, b) where GCD is the greatest common divisor.
  The greatest common divisor (GCD) of 8 and 11 is 1, since 8 and 11 are relatively prime (they share no common factors other than 1).

  Therefore, LCM(8, 11) = (8 * 11) / 1 = 88 / 1 = 88.

Because 8 and 11 are relatively prime (their greatest common divisor is 1), their least common multiple is simply their product.