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Factors and Multiples

LCM

  • The multiples of the number are the number multiplied by the natural number.
  • The common multiples of the number are the multiples that are common in two or more sets of multiples.

Example:

  • The first few multiples of the numbers 2 and 3 are
  • Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, ….

    Multiple of 3 = 3, 6, 9, 12, 18, 21, 24, 27, ……

  • The common multiples of 2 and 3 are the list of numbers common in the multiples of 2 and 3.
  • Therefore, the common multiples of 2 and 3 are: 6, 12, 18, 24, and so on.
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Least Common Multiples

  • The least common multiple is the smallest of the common multiples.
  • It is also written as LCM.

Methods to find the LCM

  • Common multiples method
  • Prime factorization method
  • Division method

Common Multiples method

  • Write the multiples of the numbers.
  • List the common multiples of the numbers.
  • Choose the smallest common multiple.

Example:

Find the least common multiples of 2 and 3

Solution:

The multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, …

The multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ….

The common multiples of 2 and 3 are 6, 12, 18, 24, 30, 36, …

The smallest of the common multiple of 2 and 3 is 6. Therefore, LCM or the least common multiple of 2 and 3 is 6.

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Prime Factorization method

  • Write the prime factorization of each number.
  • List each unique factor that appears the greatest number of times.
  • Multiply the factors.

Example:

Find the LCM of 12 and 16.

Solution:

Step 1:

Find the prime factorization of 12.

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Step 2:

Find the prime factorization of 16.

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Step 3:

12 = 2 × 2 × 3

16 = 2 × 2 × 2 × 2

LCM = 2 × 2 × 2 × 2 × 3

      = 48

Division method

  • Write the given numbers in the first line.
  • Divide the number by the smallest prime numbers.
  • Write the dividend in the next line and rewrite the number if it is not divided.
  • Repeat the process till you get a prime number with no common factors.
  • Multiply the divisor of each step.

Example:

Find the LCM of 8 and 16.

Solution:

Boy

LCM = 2 × 2 × 2 × 2

          = 8

Word Problem:

Example:

A candle seller sells candles in a packet of 12 and a candle stands in a packet of 8. What is the least number of candles and candle stand that he should sell so that there will be one candle for each stand?

Solution:

Number of candles in a packet = 12

Number of candle stands in a packet = 8

Obtain the least common multiple of 12 and 8.

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12 = 2 × 2 × 3

8 = 2 × 2 × 2

LCM = 2 × 2 × 2 × 3

      = 24

Therefore, he should sell at least 24 candles.

Fun Facts:

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Did you know?

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