What is the least common multiple of 7 28 42?

Answer 1

The traditional method is to list the multiples of each number and pick the smallest multiple they have in common. This can be very tasking for large numbers. The traditional solution is shown below:

[Method 1]

Steps:

1. List the multiples of each number:

28 - 28, 56, 84, 112, 140...

42 - 42, 84, 126, 168, 210...

2. Pick the smallest multiple they have in common which in this case is 84. If there are no common multiples, continue listing multiples until a common multiple is produced.

[Method 2 - Prime factorization Method]

Steps:

1. Find the prime factorization of each number.

28 - 2*2*7

42 - 2*3*7

2. Circle the prime factors they have in common one pair at a time.

One pair of twos and one pair of sevens.

The other 2 and 3 remain uncircled.

3. Multiply one number from each of the pairs by each of the uncircled prime factors remaining to get the LCM (least common multiple).

2*7*2*3 = 84

Answer 2

84