Find the least number which is exactly divisible by 18,24,asd36
Answers
18=2×3×3
24=2×2×2×3
36=2×2×3×3
2^3×3^2=8×9=72
Hence, the least no. which is divisible by all the three is 72
Answer:
The least number exactly divisible by 18, 24, and 36 is 72, which is the LCM of these three numbers
Step-by-step explanation:
To find the least number which is exactly divisible by 18, 24, and 36, we need to find the LCM (Least Common Multiple) of these numbers.
First, we can factor each of the given numbers into their prime factors:
18 = 2 × 3^2
24 = 2^3 × 3
36 = 2^2 × 3^2
To find the LCM, we need to take the highest power of each prime factor that appears in any of the given numbers. Therefore, the LCM of 18, 24, and 36 is:
LCM = 2^3 × 3^2 = 72
So, the least number which is exactly divisible by 18, 24, and 36 is 72.
We can verify that 72 is divisible by 18, 24, and 36 by dividing 72 by each of the given numbers and confirming that there is no remainder.
The least number exactly divisible by 18, 24, and 36 is 72, which is the LCM of these three numbers.
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