**Find the LCM of the following numbers:****(a) 9 and 4 (b) 12 and 5 (c) 6 and 5 (d) 15 and 4****Observe a common property in the obtained LCMs. Is LCM the product of two numbers in each case?**

**Solution (a)**

9 and 4

Let's find prime factors of 9 and 4.

Prime factor 3 is occurring most number of times in the prime factorization of 9.

Prime factor 2 is occurring most number of times in the prime factorization of 4.

Therefore, L.CM

**Solution (b)**

12 and 5

Let's find prime factors of 12 and 5.

Prime factor 2 is occurring most number of times in the prime factorization of 12.

Prime factor 3 is occurring most number of times in the prime factorization of 12.

Prime factor 5 is occurring most number of times in the prime factorization of 5.

Therefore, L.C.M

**Solution (c)**

6 and 5

Let's find prime factors of 6 and 5.

2 is coming most number of times in the prime factorization of 6.

3 is coming most number of times in the prime factorization of 6.

5 is coming most number of times in the prime factorization of 5.

Therefore, L.C.M

**Solution (d)**

15 and 4

Let's find prime factors of 15 and 4.

3 is coming most number of times in the prime factorization of 15.

5 is coming most number of times in the prime factorization of 15.

2 is coming most number of times in the prime factorization of 4.

Therefore, L.C.M

We can note that each L.C.M is the multiple of 3.

We can also see that L.C.M is equal to the product of given numbers. This happens when given numbers are co-prime.