Page 39 - SM Class 5 Inner.cdr

Example 14 : Find the least common Example 15 : Find the least common
multiple (L.C.M) of 20 and 30 by division multiple (L.C.M) of 50 and 75 by division
method. method.
2 20, 30 5 50, 75
Solution : Solution :
2 10, 15 5 10, 15

5 5, 15 2 2, 3
3 1, 3 3 1, 3

1, 1 1, 1
Least common multiple (L.C.M) of 20 and Least common multiple (L.C.M) of 50 and
30 = 2 × 2 × 5 × 3 = 60. 75 = 5 × 5 × 2 × 3 = 150.

E xercise 3.5

1. Find lowest common multiple of the following numbers :
a. 16, 24, 40 b. 40, 56, 60 c. 207, 138
d. 72, 96, 120 e. 120, 150, 135 f. 102, 170, 136

2. Find LCM by prime factorization.
a. 12, 27, 36 b. 5, 15, 27 c. 21, 24, 60
d. 30, 25, 65, 45 e. 81, 54, 20, 27 f. 55, 75, 95
g. 10, 25, 40, 35 h. 12, 24, 48, 72 i. 15, 25, 40, 70

j. 25, 40, 75, 90

Relationship between H.C.F. and L.C.M.

The product of the HCF and LCM of two natural numbers is equal to product of
the two numbers. Let us verify this property with the help of an example.
Take any two numbers say 15 and 18 and find their HCF and LCM.

HCF LCM
3 15, 18 2 15, 18
5, 6 3 15, 9
3 5, 3

= 3 5 5, 1 = 2 × 3 × 3 × 5 = 90
H.C.F. × L.C.M. = 3 × 90 = 270 1,1

Also, The product of these two numbers = 15 × 18 = 270
Therefore, product of H.C.F. and L.C.M. of 15 and 18 = product of 15 and 18.

So, from the above explanation we conclude that the product of highest common
factor (H.C.F.) and lowest common multiple (L.C.M.) of two numbers is equal to
the product of two numbers.
or, H.C.F. × L.C.M. = First number × Second number

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Mathematics In Focus - 5