Fast answers
1. First five multiples
a) \(4:\) 4, 8, 12, 16, 20
b) \(7:\) 7, 14, 21, 28, 35
c) \(10:\) 10, 20, 30, 40, 50
d) \(12:\) 12, 24, 36, 48, 60
e) \(17:\) 17, 34, 51, 68, 85
f) \(25:\) 25, 50, 75, 100, 125
2. First three common multiples
a) 3 and 4: 12, 24, 36
b) 4 and 7: 28, 56, 84
c) 5 and 9: 45, 90, 135
d) 6 and 7: 42, 84, 126
3. First three common multiples
a) 2, 3 and 5: 30, 60, 90
b) 4, 5 and 6: 60, 120, 180
c) 2, 5 and 9: 90, 180, 270
4. All factors
a) 7: 1, 7
b) 10: 1, 2, 5, 10
c) 16: 1, 2, 4, 8, 16
d) 24: 1, 2, 3, 4, 6, 8, 12, 24
e) 56: 1, 2, 4, 7, 8, 14, 28, 56
f) 40: 1, 2, 4, 5, 8, 10, 20, 40
g) 32: 1, 2, 4, 8, 16, 32
h) 41: 1, 41
i) 63: 1, 3, 7, 9, 21, 63
j) 75: 1, 3, 5, 15, 25, 75
k) 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
l) 64: 1, 2, 4, 8, 16, 32, 64
5. HCF
a) 4
b) 4
c) 6
d) 8
e) 8
f) 6
g) 24
h) 2
i) 15
j) 12
k) 25
l) 12
m) 15
n) 5
o) 16
p) 14
6. HCF
a) 5
b) 3
c) 4
d) 3
e) 14
f) 17
Principle:
- To find common multiples, find the LCM, then multiply it by \(1,2,3,\ldots\).
- To find the HCF, list factors or use prime factors and choose the greatest common factor.
For example, \(\mathrm{HCF}(16,20)=4\), because 4 is the largest number dividing both 16 and 20.
