LCM of 72,300,36
The prime factors of 72 are 2^3 * 3^2, the prime factors of 300 are 2^2 * 3 * 5^2, and the prime factors of 36 are 2^2 * 3^2. To find the LCM, we need to take the highest power of each prime factor that appears in the numbers. Therefore, the LCM of 72, 300, and 36 is 2^3 * 3^2 * 5^2, which equals 3600.
To find the least common multiple (LCM) of 72, 300, and 36, we need to first identify the prime factors of each number.
Prime factors of 72:
72 = 2 × 2 × 2 × 3 × 3
Prime factors of 300:
300 = 2 × 2 × 3 × 5 × 5
Prime factors of 36:
36 = 2 × 2 × 3 × 3
Next, we can determine the highest power of each prime factor that appears in any of the numbers. To find the LCM, we need to take the product of these highest powers.
Highest power of 2: 2^3
Highest power of 3: 3^2
Highest power of 5: 5^2
Now, we can calculate the LCM by multiplying these highest powers:
LCM = 2^3 × 3^2 × 5^2
= 8 × 9 × 25
= 1800
Therefore, the LCM of 72, 300, and 36 is 1800.
To find the Least Common Multiple (LCM) of 72, 300, and 36, you can follow these steps:
Step 1: Begin by listing the prime factors of each number.
- Prime factorization of 72: 2^3 * 3^2
- Prime factorization of 300: 2^2 * 3 * 5^2
- Prime factorization of 36: 2^2 * 3^2
Step 2: Identify the highest power of each prime factor that appears in any of the numbers.
- The highest power of 2: 3 (from 2^3)
- The highest power of 3: 2 (from 3^2)
- The highest power of 5: 2 (from 5^2)
Step 3: Multiply the prime factors raised to their highest powers found in step 2.
- LCM = 2^3 * 3^2 * 5^2
= 8 * 9 * 25
= 1800
Therefore, the LCM of 72, 300, and 36 is 1800.