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\\November 3, 2023 11:27 AM Surender Prajapati Proof 5 Reader _________________________ Date: ___________________74

Example 3: Find the LCM of 15, 20, 25 and 45 using division method.
Solution: We have 15, 20, 25 and 45.

Step 1: Write 15, 20, 25 and 45 in a row. 3 15, 20, 25, 45
Step 2: Choose the smallest suitable prime number, 5 5, 20, 25, 15

which divides 15 and 45 exactly. 2 1, 4, 5, 3
Step 3: Write the quotient below the numbers and the 2 1, 2, 5, 3

numbers which cannot divide by 3, bring it down 3 1, 1, 5, 3
to the next row as it is. 5 1, 1, 5, 1
Step 4: Next, the suitable prime number is 5; divide the 1, 1, 1, 1
numbers by 5.

Step 5: Continue dividing till you get 1 as quotient for all the numbers.

Thus, the LCM of 15, 20, 25 and 45 = 3 × 5 × 2 × 2 × 3 × 5 = 900.
Example 4: Find the LCM of:

(a) 20, 60 and 90 (b) 24, 40 and 72

Solution: (a) 2 20, 60, 90 (b) 2 24, 40, 72
2 10, 30 45 2 12, 20, 36
3 5, 15, 45 2 6, 10, 18
5 5, 5, 15 3 3, 5, 9
3
3 1, 5,
3 1, 1, 3 5 1, 5, 1
1, 1, 1 1, 1, 1

LCM = 2 × 2 × 3 × 3 × 5 LCM = 2 × 2 × 2 × 3 × 3 × 5
= 180 = 360

Practice Time 3F

1. Write the common multiples of each pair of numbers. Circle their smallest common
multiple.

(a) 12, 20 (b) 16, 24 (c) 14, 21 (d) 18, 30 (e) 10, 15
2. Find the LCM of these numbers using the common multiples method.

(a) 21, 28 (b) 48, 72 (c) 22, 110 (d) 60, 63

(e) 24, 36 (f) 38, 57 (g) 12, 15, 18 (h) 20, 30, 50
(i) 20, 32, 40 (j) 11, 22, 33 (k) 12, 15, 40 (l) 12, 16, 32

3. Find the LCM of these numbers using the prime factorisation method.

(a) 14, 17 (b) 51, 54 (c) 78, 82 (d) 25, 75
(e) 54, 90 (f) 24, 72 (g) 18, 20, 32 (h) 12, 16, 30

(i) 21, 24, 36 (j) 3, 15, 60 (k) 33, 55, 99 (l) 12, 18, 24

74 Mathematics-5