Mathematics Form 1-4 : CHAPTER FIVE – LEAST COMMON MULTIPLE

Specific Objectives

By the end of the topic, the learner should be able to:

1. List multiples of numbers.
2. Find the LCM of a set of numbers.
3. Apply knowledge of LCM in real-life situations.

Content

1. Multiples of a number
2. LCM of a set of numbers
3. Application of LCM in real-life situations

Introduction

Definition

LCM or Least Common Multiple is the smallest multiple that two or more numbers divide into evenly, i.e., without a remainder. A multiple of a number is the product of the original number and another number.

Some multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, and so on.

Some multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, and so forth.

A Common Multiple is a number that is divisible by two or more numbers. Some common multiples of 4 and 7 are 28, 56, 84, and 112.

When looking for the Least Common Multiple, you are searching for the smallest multiple that both numbers divide into evenly. The least common multiple of 4 and 7 is 28.

Example

Find the L.C.M of 8, 12, 18, and 20.

Solution

The L.C.M is the product of all the divisions used. Therefore, the L.C.M of 8, 12, 18, and 20 = 2 × 2 × 2 × 3 × 3 × 5 = 360.

Note: Unlike the G.C.D tables, if the divisor/factor does not divide a number exactly, then the number is retained. For example, 2 does not divide 9 exactly; therefore, 9 is retained. The last row must have all values equal to 1.

End of topic

Did you understand everything? If not, ask a teacher, friends, or anybody and make sure you understand before going to sleep!

Past KCSE Questions on the topic

Find the L.C.M of x² + x, x² – 1, and x² – x.

1. Find the least number of sweets that can be packed into polythene bags which contain either 9, 15, 20, or 24 sweets with none left over.
2. A number n is such that when it is divided by 27, 30, or 45, the remainder is always 3. Find the smallest value of n.
3. A piece of land is to be divided into 20 acres, 24 acres, or 28 acres for farming and leave 7 acres for grazing. Determine the smallest size of such land.
4. When a certain number x is divided by 30, 45, or 54, there is always a remainder of 21. Find the least value of the number x.

A number m is such that when it is divided by 30, 36, and 45, the remainder is always 7. Find the smallest possible value of m.