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4. Find the LCM of these numbers using the division method.
(a) 4, 24, 32 (b) 24, 42, 72 (c) 20, 60, 90 (d) 18, 36, 48

(e) 9, 13, 26 (f) 18, 9, 27 (g) 32, 16, 50 (h) 14, 35, 49

5. Two bulbs flash at regular intervals of 42 and 77 seconds respectively. They first
flash together at 10:45 p.m. At what time will they flash together:

(a) Second time? (b) Fifth time?

6. Sia has a collection of hair bands and she wants to arrange them in groups of 4, 6 or
8 with no hair band left behind. Find the number of hair bands she has.

7. Two bells ring at intervals of 24 min and 36 min respectively. If they ring at 8:15 a.m.,
when will they ring together next?

RELATIONSHIP BETWEEN HCF AND LCM

Consider any two numbers say 18 and 24. Let us find their HCF and LCM.

HCF of 18 and 24 LCM of 18 and 24

18 24 1 2 18, 24
– 18 2 9, 12
6
2 9,
6 18 3 3 9, 3
– 18 3 3, 1
0 1, 1

So, HCF of 18 and 24 = 6 and LCM = 2 × 2 × 2 × 3 × 3 = 72
Product of HCF × LCM = 6 × 72 = 432

Now, product of given two numbers = 18 × 24 = 432.
What do you observe? Clearly, product of HCF and LCM of two numbers = product of their

numbers.
nd
st
Thus, HCF × LCM = 1 number × 2 number
This relationship between HCM and LCM is useful for solving many problems.

Example 1: The HCF and LCM of two numbers are 15 and 180 respectively. If one of the
numbers is 45, find the other number.

Solution: Given that, HCF = 15, LCM = 180 and one number = 45
st
nd
We know that, HCF × LCM = 1 number × 2 number.
nd
Here, 15 × 180 = 45 × 2 number
nd
2700 = 45 × 2 number
So, 2 number = 2700 = 60
nd
45
Thus, the other number is 60.

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