Find L.C.M of 9, 18, 36.

To find the Least Common Multiple (L.C.M) of the numbers 9, 18, and 36, we can use the prime factorization method.

Step 1: Prime Factorization

First, we break down each number into its prime factors:

• 9: 3 × 3 or 3²
• 18: 2 × 3 × 3 or 2 × 3²
• 36: 2 × 2 × 3 × 3 or 2² × 3²

Step 2: Identify the Highest Powers

Next, we take the highest power of each prime number from the factorizations:

• For 2: the highest power is 2² (from 36)
• For 3: the highest power is 3² (from all three numbers)

Step 3: Calculate the L.C.M

Now, we multiply these highest powers together:

L.C.M = 2² × 3² = 4 × 9 = 36

Final Result

The Least Common Multiple of 9, 18, and 36 is 36.