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# LEAST COMMON MULTIPLE

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## LEAST COMMON MULTIPLE

LEAST COMMON MULTIPLE:Specific Objectives

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

• List multiples of numbers.
• Find the L CM of a set of numbers.
• Apply knowledge of L CM in real life situations.

Content

• Multiples of a number
• L CM of a set of numbers
• Application of L CM in real life situations.

Introduction

Definition

LCM or LCF 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 with another number.

Some multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56 …

Some multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56 …

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 looking for the smallest multiple that they both 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

 8 18 20 2 4 6 10 2 2 3 5 2 1 3 5 3 1 1 5 3 1 1 5 5 1 1 1

The L.C.M is the product of all the divisions used.

Therefore, L.C.M. of 8, 12, 18 and 20 = 2 x 2 x 2 x 3 x 3 x5

= x 5

= 360

Note;

Unlike the G.C.D tables, if the divisor /factor does not divide a number exactly, then the number is retained, e.g., 2 does not divide 9 exactly, therefore 9 is retained .The last row must have all values 1.

Past KCSE Questions on the topic

• Find the L.C.M of x2 + x, x2 – 1 and x2 – x .
• Find the least number of sweets that can be packed into polythene bags which contain either 9 or 15 or 20 or 24 sweets with none left over.
• 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.
• A piece of land is to be divided into 20 acres or 24 acres or 28 acres for farming and

Leave 7 acres for grazing. Determine the smallest size of such land.

• 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.

ALL MATHEMATICS NOTES FORM 1-4 WITH TOPICAL QUESTIONS & ANSWERS

PRIMARY NOTES, SCHEMES OF WORK AND EXAMINATIONS

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