Find the LCM of each of the following group of numbers by prime factorisation.
(c) 300, 400, 700
Answers
Answer:
L.C.M. of 18, 24 and 96
(i) By prime factors
Prime factors of 18 = 2 x 3 x 3
Prime factors of 24 = 2 x 2 x 2 x 3
Prime factors of 96 = 2 x 2 x 2 x 2 x 2 x 3
L.C.M. = 2 x 2 x 2 x 2 x 2 x 3 x 3 = 288
By common division method
L.C.M. of 18, 24 and 96 = 2 x 2 x 2 x 3 x 3 x 4 = 288
(ii) 100, 150 and 200
Factor of 100 = 2 × 2 × 5 × 5 = 22 × 52
Factor of 150 = 2 × 3 × 5 × 5
= 21 × 31 × 52
Factor of 200 = 2 × 2 × 2 × 5 × 5 = 23 × 52
∴ L.C.M. OF 100, 150 and 200
= 23 × 31 × 52 = 600
∴ L.C.M. OF 100,
(iii) 14, 21, 98
Factor of 14 = 2 × 7 = 21 × 71
Factor of 21 = 3 × 7 = 31 × 71
Factor of 98 = 2 × 7 × 7 = 21 × 72
∴ L.C.M. of 14, 21 and 98
= 21 × 31 × 72 = 294
(v) 34, 85 and 51
Factor of 34 = 2 ×17 = 21 × 171
Factor of 85 = 5 × 17 = 51 × 171
Factor of 51 = 3 × 17 = 31 × 171
∴ L.C.M. of 34, 85 and 51
= 21 × 51 × 31 × 17 = 510
∴ L.C.M. OF 34, 85 and 51
= 2 × 17 × 5 × 3 = 510
Answer:
Correct answer os 8400.
The LCM of 300, 400, 700 is 8400.
See the attached image.
