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Mathematics

Find the LCM of the given numbers by division method:
(i) 480, 672
(ii) 6, 8, 45
(iii) 24, 40, 84
(iv) 20, 36, 63, 77

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Answer

(i) 480, 672

2	480, 672
2	240, 336
2	120, 168
2	60, 84
2	30, 42
3	15, 21
5	5, 7
7	1, 7
	1, 1

Hence, LCM of 480 and 672 = 2 × 2 × 2 × 2 × 2 × 3 × 5 × 7 = 3360.

(ii) 6, 8, 45

2	6, 8, 45
2	3, 4, 45
2	3, 2, 45
3	3, 1, 45
3	1, 1, 15
5	1, 1, 5
	1, 1, 1

Hence, LCM of 6, 8 and 45 = 2 × 2 × 2 × 3 × 3 × 5 = 360.

(iii) 24, 40, 84

2	24, 40, 84
2	12, 20, 42
2	6, 10, 21
3	3, 5, 21
5	1, 5, 7
7	1, 1, 7
	1, 1, 1

Hence, LCM of 24, 40 and 84 = 2 × 2 × 2 × 3 × 5 × 7 = 840.

(iv) 20, 36, 63, 77

2	20, 36, 63, 77
2	10, 18, 63, 77
3	5, 9, 63, 77
3	5, 3, 21, 77
5	5, 1, 7, 77
7	1, 1, 7, 77
11	1, 1, 1, 11
	1, 1, 1, 1

Hence, LCM of 20, 36, 63 and 77 = 2 × 2 × 3 × 3 × 5 × 7 × 11 = 13860.

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