Page 59 - Start Up Mathematics_5

Example 24: The HCF of two numbers is 6. Their LCM is 120. If one number is 24, find the
other number.

Solution: First number = 24, HCF = 6, LCM = 120 Working
3 0
HCF × LCM 6 × 120 720
Second number = = = = 30 24 7 2 0
First number 24 24 – 7 2 ↓
So, the other number is 30. 0 0
– 0
0
EXERCISE 3.4

1. Find the LCM of the following numbers by prime factorization.

(a) 12 and 18 (b) 20 and 22 (c) 32 and 48
(d) 55 and 105 (e) 64 and 78 (f) 26, 42 and 66
(g) 98, 112 and 144 (h) 48, 64 and 120 (i) 75, 125 and 275

2. Find the LCM of the following numbers by division method.
(a) 16 and 28 (b) 36 and 44 (c) 52 and 128

(d) 45 and 120 (e) 10, 15 and 30 (f) 20, 60 and 80
(g) 80, 140 and 200 (h) 111, 243 and 729

3. The LCM of 25 and 65 is 325. Find their HCF.
4. The LCM of two numbers is 1,344 and their HCF is 4. If one of the numbers is 84, find
the other number.

Word Problems

Example 25: Three strings of lengths 240 cm, 318 cm and 426 cm are to be cut into equal
lengths. What is the greatest possible length of each piece?

Solution: We need to find the HCF of 240 cm, 318 cm and 426 cm.
1 7 1
240 3 1 8 6 4 2 6
– 2 4 0 3 – 4 2 ↓
7 8 2 4 0 0 6
– 2 3 4 1 3 – 6
6 7 8 0
– 6 ↓
1 8
– 1 8
0

The HCF of 240 cm, 318 cm and 426 cm is 6 cm.

Hence, the greatest possible length of each piece is 6 cm.

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