What is the LCM of 6 and 10?

To find the LCM (Least Common Multiple) of 6 and 10, we can use different methods, such as listing out the multiples of both numbers and finding the smallest one that they have in common, or by using the prime factorization method.

Method 1: Listing multiples

• Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, …
• Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, … The smallest multiple that they have in common is 30. Therefore, the LCM of 6 and 10 is 30.

Method 2: Prime factorization

• Prime factorization of 6: 2 x 3
• Prime factorization of 10: 2 x 5
• LCM = product of highest powers of all prime factors involved.
• In this case, the prime factors involved are 2, 3, and 5.
• The highest power of 2 is 2¹, the highest power of 3 is 3¹, and the highest power of 5 is 5¹.
• Therefore, LCM(6,10) = 2¹ x 3¹ x 5¹ = 30.

Either method gives the same result, which is 30.