Given that the LCM of 306 and 657 is 22338, what is the LCM of 102, 306, and 657? (a) 1 (b) 22338 (c) 22338 x 102 (d) None of these

Methods to find LCM

There are three key approaches we can use to determine the LCM of two or more numbers. As follows:

Listing the Multiples: The first step in determining the least common multiple of any given set of numbers is to make a list of all the multiples of those numbers. The next step is to determine the first common multiple between those multiples.

Prime Factorization Method: This technique finds the product of three numbers by writing their prime factors together.

Division Approach: The product of all the prime numbers we acquired through the division method will be the LCM of the numbers.

LCM and HCF relationship

The two key mathematical methods are LCM and HCF. The least common multiples (LCM) of two or more numbers are discovered using this method, whereas the highest common factor (HCF) is discovered using this method. However, the following formulas can relate to both:

LCM(a,b) = a × b / GCF(a,b)

GCF(a,b) = a × b / LCM(a,b)

Where a and b are the two numbers.

Summary:

Given that the LCM of 306 and 657 is 22338, what is the LCM of 102, 306, and 657?(a) 1(b) 22338(c) 22338 x 102(d) None of these

Given that the LCM of 306 and 657 is 22338, the LCM of 102, 306, and 657 is 22338. LCM can be found using three methods like division, prime factorization, and listing multiples.