Page 66 - ICSE Math 6

Example 30: Find the LCM of 42, 70 and 210 using the division method.

Solution: 2 42, 70, 210
3 21, 35, 105
5 7, 35, 35
7 7, 7, 7

1, 1, 1
∴ LCM = 2 × 3 × 5 × 7 = 210

Example 31: Find the smallest number which is exactly divisible by 24, 54, 25 and 75.
Solution: The required number is the LCM of 24, 54, 25 and 75.
2 24, 54, 25, 75

3 12, 27, 25, 75
5 4, 9, 25, 25
5 4, 9, 5, 5
4, 9, 1, 1

∴ LCM = 2 × 3 × 5 × 5 × 4 × 9 = 5,400
Example 32: Find the smallest number which when divided by 22, 36 and 54 leaves 5 as the remainder
in each case.
Solution: The smallest number divisible by 22, 36 and 54 is the LCM of 22, 36 and 54.

2 22, 36, 54
3 11, 18, 27
3 11, 6, 9
11, 2, 3

∴ LCM = 2 × 3 × 3 × 11 × 2 × 3 = 1,188
The required number leaves 5 as the remainder each time when divided by 22, 36 and 54.
Therefore, the required number is 1,188 + 5 = 1,193.
Example 33: Salma, David and Tarun start walking. Their steps measure 72 cm, 81 cm and 90 cm
respectively. What is the minimum distance that each of them can cover in complete
steps?

Solution: Measures of their steps are 72 cm, 81 cm and 90 cm. The
minimum distance that each of them can cover in complete 2 72, 81, 90
steps can be obtained by finding the LCM of 72, 81 and 90. 3 36, 81, 45
3 12, 27, 15
Now, LCM = 2 × 3 × 3 × 4 × 9 × 5 = 3,240 4, 9, 5
Hence, the least distance that each of them can cover in complete
steps is 3,240 cm.

Example 34: Determine the greatest 4-digit number which is exactly divisible by 8, 10 and 12.

Solution: To get the desired number let’s first find the LCM of 8, 10 and 12. 2 8, 10, 12
The LCM of 8, 10 and 12 = 2 × 2 × 2 × 5 × 3 = 120 2 4, 5, 6
2, 5, 3

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