Selina Concise Class 6 Math Chapter 8 H.C.F. and L.C.M. Exercise 8(C) Solution
EXERCISE 8C
(1) Using the common multiple method find the LCM of the following:
(i) Solution:
Multiples of 8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80….
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 120….
Multiples of 24 = 24, 48, 52, 96, 120, 144, 168 …..
Required LCM = 24.
(ii) Solution: Multiples of 10 = 10, 20, 30, 40, 50, 60 , 70, 80, 90, 100….
Multiples of 15 = 15, 30, 45, 60, 75, 90, 105, 120…..
Multiples of 20 = 20, 40, 60, 80, 100, 120, 140 160….
Required LCM = 60
(iii) Solution: Multiples of 3 = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 11, 36….
Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 …..
Multiples of 9 = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 …..
Multiples of 12 = 12, 24, 36, 48, 60, 72, 84, 96, 120….
Required LCM = 36
(2) Find the LCM of each of the following groups of number using (i) the prime factor method (ii) the common division method:
The prime factor method
(i) 18 = 2 × 3 × 3
24 = 2 × 2 × 2 × 3
96 = 2 × 2 × 2 × 2 × 2 × 3
∴ Required L.C.M. = 2 × 2 × 2 × 2 × 2 × 3 × 3 = 288
(ii) 100 = 2 × 2 × 5 × 5
150 = 2 × 3 × 5 × 5
200 = 2 × 2 × 2 × 5 × 5
∴ Required L.C.M. = 2 × 2 × 2 × 3 × 5 × 5 = 600
(iii) 14 = 2 × 7
21 = 3 × 7
98 = 2 × 7 × 7
∴ Required L.C.M. = 2 × 3 × 7 × 7 = 294
(iv) 22 = 2 × 11
121 = 11 × 11
33 = 3 × 11
∴ Required L.C.M. = 2 × 3 × 11 × 11 = 726
(v) 34 = 2 × 17
85 = 5 × 17
51 = 3 × 17
∴ Required L.C.M. = 2 × 3 × 5 × 17 = 510
(3) Solution: We know that, H.C.F. × L.C. M = Product of two numbers
Let the other number be x.
⇒ 150 × x = 50 × 300
⇒ 150x = 15000
⇒ x = 100
The other number is 100.
(4) Solution: We know that, H.C.F. × L.C. M = Product of two numbers
Let the H.C.F be x.
⇒ 72 × x = 432
⇒ x = 6
Therefore, the H.C.F. is 6.
(5) Solution: We know that, H.C.F. × L.C. M = Product of two numbers
Let the L.C.M. be x.
⇒ 40 × x = 19200
⇒ x = 480
(6)
So, 360 is the smallest number which on dividing by 12, 15, 18, 24 and 36 leaves no remainder.
(7)
So, the required number is (1440 + 1) = 1441.
(8)
So, the required number is (864 – 3) = 861.