What is the Least Common Multiple of 9 and 42?

The LCM of 9 and 42 is 126. Steps to find LCM: Find the prime factorization of 9 (9 = 3 × 3) and 42 (42 = 2 × 3 × 7); Multiply each factor with its highest exponent and multiply them together; The LCM of 9 and 42 is 126.

Methods to Find LCM of 9 and 42

The LCM of 9 and 42 can be found by using the following methods: Prime Factorization Method, Division Method, List of Multiples Method.

Prime Factorization Method: Find the prime factorization of 9 (9 = 3 × 3) and 42 (42 = 2 × 3 × 7); Multiply each factor with its highest exponent and multiply them together; The LCM of 9 and 42 is 126.

Division Method: Divide 9 and 42 by their greatest common factor (GCF). The GCF of 9 and 42 is 3. 9/3 = 3 and 42/3 = 14. Then, multiply the two quotients to get the LCM of 9 and 42, which is 3 × 14 = 42.

List of Multiples Method: List out the multiples of both numbers and find the smallest multiple that is common to both numbers. For example, the multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72… and the multiples of 42 are 42, 84, 126, 168… From the list, we can see that the smallest multiple that is common to both numbers is 126. Thus, the LCM of 9 and 42 is 126.

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