New Learning Composite Mathematics SK Gupta Anubhuti Gangal Class 6 Playing With Numbers Self Practice 3H Solution
(1) (a) Multiples of = 2: 2,4,2,8…
Multiple of = 3: 3,6,9,12…..
L.C.M of 2 and 3 = 6
(b) 6 = 2×2
10 = 2×5
L.C.M of 6 and 10 = 2x3x5= 30
(c) 9 = 32
15 = 3×5
L.C.M of 9 and 15 = 32x5
= 45
(d) 4=22
14=2×7
L.C.M of 4 and 14 = 22x7
= 28
(e) 12 = 22x3
32 = 25
L.C.M of 12 and 32= 25 x3
= 96
(f) 25 = 52
100 = 52 x 22
L.C.M of 25 and 100 = 52 x 22= 100
(4) (a) The LCM is the dividend
eg – LCM of 2 and 4 is 4
(b) When they have no common factor or when they are co-prime numbers
eg – 4 and 9 or 3 and 7
(c) Because they are infinitely many common multiples of a group of numbers.
(d) No, the LCM of a group of numbers can be equal to one of the smaller than any numbers in the group.
eg – LCM of 6 and 12 is 12 but never smaller than any number in the group.
(e) The LCM is the least common multiple of all numbers in a given group. It is the least number which is divisible by all of them.
The GCF is the greatest common factor of all numbers which devides exactly all of them.