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Division Method

Follow these steps to find the LCM of two or more numbers by division method.

Step 1: Write the given numbers in a row separating them by commas.

Step 2: Divide them by a suitable prime number that exactly divides at least two of the given
numbers.
Step 3: Put the quotient directly under the numbers in the next row. If the number is not
divided exactly, bring it down as it is.

Step 4: Continue the process of Step 2 and Step 3 until all the co-prime numbers or 1 are left
in the last row.

Step 5: Multiply all the divisors (primes) and the quotients in the last row to get the LCM.

Example 27: Find the LCM of 8, 15 and 24.
Solution: By division method,

2 8, 15, 24 Here 2 can divide 8 and 24 exactly. Bring down 15 as it is.
2 4, 15, 12 Again, divide 4 and 12 by 2.

2 2, 15, 6 Again, divide 2 and 6 by 2.
3 1, 15, 3 Here, 3 can divide 15 and 3 exactly.

1, 5, 1 Stop.

Now, find the product of all the divisors and the quotients (except 1) in the last row.

Thus, the LCM of 8, 15 and 24 = 2 × 2 × 2 × 3 × 5 = 120.

Example 28: Find the smallest number which when divided by 32, 28, 36 and 40, leaves remainder
4 in each case.

Solution: 2 32, 28, 36, 40 Think and Answer

2 16, 14, 18, 20 Find the smallest 4-digit number
2 8, 7, 9, 10 which is divisible by 18, 24 and 32.

4, 7, 9, 5

The LCM of the given numbers = 2 × 2 × 2 × 4 × 7 × 9 × 5 = 10080
So, the required number is 10080 + 4 = 10,084

Example 29: Find the greatest 3-digit number exactly divisible by 8, 10 and 12.

Solution: We know that the greatest 3-digit number is 999. But it is not exactly 2 8, 10, 12
divisible by 8, 10 and 12.
2 4, 5, 6
The least number exactly divisible by 8, 10 and 12 is their LCM and 2, 5, 3
the required number would be the multiple of this LCM.
Here, LCM of 8, 10 and 12 = 2 × 2 × 2 × 5 × 3 = 120

165 Prime Time