Least Common Multiple

LCM – Definition

A common multiple is a number that is a multiple of two or more numbers.

The least common multiple is the smallest multiple shared between two or more numbers.

The Least Common Multiple (LCM) is also referred to as the Least Common Denominator (LCD).

Finding The Least Common Multiple

Example

Let’s take an example – What is the LCM of 24 and 32?

First, we factor both numbers into their primes.

The prime factorization of 24 is
24 = 2 x 2 x 2 x 3

The prime factorization of 32 is
32 = 2 x 2 x 2 x 2 x 2

Next, we identify any shared primes.

With 24 and 32, 2 x 2 x 2 is a shared prime number.

Then, we take the shared prime and multiply it with all of the other prime factors.

(2 x 2 x 2)  x 3 x  2 x 2

The red number 2 x 2 x 2 is the shared prime factor.
The blue numbers are the other prime factors.

Hence we get the LCM of 32 and 24 is 96.

Check Point

Question 1

Find the L.C.M. of 12, 27

Question 2

Find the L.C.M. of 125,64,8

Question 3

Quincy is buying flower bulbs for his garden. He wants to buy the same number of tulips and daffodils. If tulip bulbs come in packs of 28 and daffodil bulbs come in packs of 42, what is the least number of each type of bulb Quincy will need to buy?

Question 4

In a morning walk, three persons step off together. Their steps measure 85 cm, 70 cm, and 90 cm respectively. What is the minimum distance each should walk so that all can cover the same distance in complete steps?

Question 5

The traffic lights at three different road crossings change after every 12 seconds, 18 seconds, and 22 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change simultaneously again?

Grade 6 Science Worksheets

• Inquiry process
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• Biotic and Abiotic Factors
• Impact of Organisms
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Grade 6 Math Worksheets

• Probability
• Ratio
• Sequence & Patterns
• Division Word Problems  (New)
• Solving two step equations (New)
• One Step Equation  (New)
• Place Value  (New)
• Two Step Equation  (New)
• To convert percents to decimals and vice versa  (New)
• To convert Percents to Fractions and vice versa  (New)