Lesson 1, Topic 4
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# Lowest Common Multiple

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

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 error: