Lesson 1, Topic 4
In Progress

# Lowest Common Multiple

Lesson Progress
0% Complete

The lowest common multiple of two or more numbers is the lowest multiple they have in common.

For example:

The multiples of 2 are  2, 4, 6, 8, 190, 12, 14, 16, 18……

The multiples of 3 are 3, 6, 9, 12, 15, 18 …….

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

The lowest common multiple of 2 and 3 is 6;

### Example

Find the LCM of

a. 3, 7 and 10

b. 2, 3 and 4

c.
23 x 32 x 5
22 x 3 x 5

d.
24 x 32 x 5 x 7 x 112
23 x 5 x 73 x 11
22 x 33 x 5 x 72 x 11

Solution

a.

1st Method

LCM  = 2 x 3 x 5 x 7

= 6 x 35

=  210

2nd Method: Find the prime factors of the given numbers.

3 = 1 × 3
7 = 1 × 7
10 = 2 × 5

∴ L.C.M. = 1 x 2 x 3 x 7 x 5

= 210

b.

LCM  of 3 and 4 = 2 x 2 x 3 = 12

c.

23 x 32 x 5
22 x 3 x 5

In this case, compare the index (power) of numbers with the same base. The numbers with greater power (index) are the common multiple.

23 x 32 x 5

22 x 3 x 5

= 23  x   32   x   5

LCM   =   23   x  32   x  5

d.

24 x 32 x 5 x 7 x 112
23 x 5 x 73 x 11
22 x 33 x 5 x 72 x 112

LCM   =   24   x  33   x  5  x  73   x  112

Evaluation Questions:

1. Find all the factors of 48

2. Find the factors of 100 that are

i. Odd numbers
ii. Even numbers
iii. Multiples of 2
iv.  Multiples of 5

3. Write down the first six multiples of 7

4. Express the following numbers as a product of prime factors.

a. 64
b.  120
c.  500
d.   980

5. Express  24 x 36  as a product of its prime factors in index form.

6. Find the common factors of the following:

a. 16 and 30
b. 36 and 50

7. Find the HCF of:

a. 4 and 12
b. 9, 18 and 54
c. 36 and 81

8. Find the HCF of

a. 22 x 32 x 53 x 7  and 24 x 35 x 5 x 72

b. 52 x 73  and  53 x 74

9. Find the first three common multiples of

a. 5 and 6
b. 2,  3  and 4

10. Find the LCM of

a. 12, 18 and 36
b. 5,  10, and 15
c. 52 x7 x 11,    2 x 3 x 5  x 11
d. 23  x 3  x 53;        2 x 32 x  52;      23  x 33  x  5 x 72

#### Responses error: