## Least Common Multiple

LEAST COMMON MULTIPLE (L.C.M)

APPLICATIONS OF L.C.M IN REAL LIFE SITUATIONS

BACKGROUND KNOWLEDGE

Multiples of 2 are: 2 ,4, 6, 8, 10, 12, 14, 16, 18 e.t.c

Multiples of 3 are: 3, 9, 12, 15, 21, 24, 27, 81, 243 e.t.c

Multiples of 5 are: 5, 10, 15, 20, 25, 30, 35,40,45, e.t.c

LEAST COMMON MULTIPLE (L.C.M)

APPLICATIONS OF L.C.M IN REAL LIFE SITUATIONSBACKGROUND KNOWLEDGE

Multiples of 2 are: 2 ,4, 6, 8, 10, 12, 14, 16, 18 e.t.c

Multiples of 3 are: 3, 9, 12, 15, 21, 24, 27, 81, 243 e.t.c

Multiples of 5 are: 5, 10, 15, 20, 25, 30, 35,40,45, e.t.c

EXERCISE

1. Joyce stride covers 50 cm and John's covers 60 cm, what is the least width of a road that each one of them can cross at exact number of strides?

2. Find the smallest sum of money that an exact multiple of

Kshs. 56, Kshs. 32 and Kshs. 48.

3. Find the smallest mass that can be measured out in

equal amounts of 6g, 8g or 9 g

4. Trees are planted on both sides of a road at 30m apart on one side and 45 apart on the other side. At one point of the road, two trees are directly opposite each other. After what distance measured from that point would a pair of trees are directly opposite each other.

**END**

Lesson Objectives

#### By the end of the lesson you should be able to

;apply the knowledge of LCM in solving real

life situations correctly.

LEAST COMMON MULTIPLE (L.C.M)

Introduction

The smallest natural number that each one of a pair of natural numbers divides into a whole number of times is called their lowest common multiple.(L.C.M)

In order to find the LCM of two or more numbers:

i. List the multiples of each of the numbers,

ii. List the common multiples of two or more numbers

iii. The smallest of the common multiples is the L.C. M

The LCM can also be found from the prime factorisation of each of the two or more numbers.

L.C.M of the numbers using multiples of numbers

Find the LCM of the following set of numbers:

a). 3 and 4

b). 5 and 7

c). 3, 4, and 5

a).

The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39 ...

The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44,...

The common multiples are 12, 24, 36 ...

The least common multiple (L.C.M) is 12

b).

The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55,60, 65, 70 ....

The multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77 ...

The common multiples are 35, 70, ...

The least common multiple (L.C.M) is 35

c).

The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39,

42,45, 48, 51, 54, 57, 60, 63, 69...

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

60, 64, 68, 72, 76 ...

The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65,

70, 75...

The common multiple is 60

The LCM is 60

L.C.M using prime factorisation method

Find the LCM of the following set of numbers using prime factorization method:

a. 15, 18

b. 2, 7, 9

c. 6, 12, 18, 36

Solutions

**a). **

15 = 3 x 5

18 = 2 x 3 x 3

The LCM is 2 x 3 x 3 x 5 = 2 x 9 x 5

= 2 x 45

= 90

**b).**

2 = 2 x 1

7 = 7 x 1

9 = 3 x 3

The LCM is 2 x 7 x 3 x 3 = 126

**c). **

6 = 2 x 3

12 = 2 x 2 x3

18 = 2 x 3 x 3

36 = 2 x 2 x 3 x 3

The L.C.M is 2 x 2 x 3 x3 = 4 x 9 = 36

Method 2

PRIME FACTORIZATION METHOD

Find the LCM of the following set of numbers using prime factorization method:

a. 15, 18

b. 2, 7, 9

c. 6, 12, 18, 36

Solutions

a).

15 = 3 x 5

18 = 2 x 32

The LCM is 2 x 32 x 5 = 2 x 9 x 5

= 2 x 45

= 90

b). 2 = 2 x 1 7 = 7 x 1 9 = 32

The LCM is 2 x 7 x 32 = 126

c). 6 = 2 x 3

12 = 22 x3

18 = 2 x 32

36 = 22 x 32

The L.C.M is 22 x 32 x 5 = 4 x 9 = 36

LEAST COMMOM MULTIPLES(L.C.M)

Least Commmon Multiples are quite easy to learn. Buckle down as you discover their usage in normal daily life

LEAST COMMOM MULTIPLES(L.C.M)

Least Commmon Multiples are quite easy to learn. Buckle down as you discover their usage in the normal daily life

Least Common Multiple

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