Math worksheet for practicing LCM and HCF problems.

I. Find the highest common factor of the following by complete factorisation:

(i) 24, 56, 64
Prime factorisation:
24 = 2³ × 3
56 = 2³ × 7
64 = 2⁶
HCF = 2³ = 8

(ii) 54, 198, 360
54 = 2 × 3³
198 = 2 × 3² × 11
360 = 2³ × 3² × 5
HCF = 2 × 3² = 18

(iii) 172, 68, 176
172 = 2² × 43
68 = 2² × 17
176 = 2⁴ × 11
HCF = 2² = 4

(iv) 1574, 276
1574 = 2 × 787
276 = 2² × 3 × 23
HCF = 2

(v) 405, 780, 513
405 = 3⁴ × 5
780 = 2² × 3 × 5 × 13
513 = 3³ × 19
HCF = 3

II. Find the H.C.F. by long division method:

(i) 84, 144
144 ÷ 84 = 1 remainder 60
84 ÷ 60 = 1 remainder 24
60 ÷ 24 = 2 remainder 12
24 ÷ 12 = 2 remainder 0
HCF = 12

(ii) 120, 158
158 ÷ 120 = 1 remainder 38
120 ÷ 38 = 3 remainder 6
38 ÷ 6 = 6 remainder 2
6 ÷ 2 = 3 remainder 0
HCF = 2

(iii) 433, 516, 817
First, 516 ÷ 433 = 1 remainder 83
433 ÷ 83 = 5 remainder 18
83 ÷ 18 = 4 remainder 11
18 ÷ 11 = 1 remainder 7
11 ÷ 7 = 1 remainder 4
7 ÷ 4 = 1 remainder 3
4 ÷ 3 = 1 remainder 1
3 ÷ 1 = 3 remainder 0
HCF of 433 and 516 = 1
Now, HCF of 1 and 817 = 1
HCF = 1

(iv) 622, 790, 869
622 and 790:
790 ÷ 622 = 1 remainder 168
622 ÷ 168 = 3 remainder 118
168 ÷ 118 = 1 remainder 50
118 ÷ 50 = 2 remainder 18
50 ÷ 18 = 2 remainder 14
18 ÷ 14 = 1 remainder 4
14 ÷ 4 = 3 remainder 2
4 ÷ 2 = 2 remainder 0
HCF of 622 and 790 = 2
Now, 869 ÷ 2 = 434 remainder 1
HCF of 2 and 869 = 1
HCF = 1

(v) 291, 592, 776
291 and 592:
592 ÷ 291 = 2 remainder 10
291 ÷ 10 = 29 remainder 1
10 ÷ 1 = 10 remainder 0
HCF of 291 and 592 = 1
Now, 776 ÷ 1 = 776 remainder 0
HCF = 1

(vi) 219, 1322, 2202, 8526
First, 1322 ÷ 219 = 6 remainder 8
219 ÷ 8 = 27 remainder 3
8 ÷ 3 = 2 remainder 2
3 ÷ 2 = 1 remainder 1
2 ÷ 1 = 2 remainder 0
HCF of 219 and 1322 = 1
Now, 2202 ÷ 1 = 2202 remainder 0
HCF = 1
8526 ÷ 1 = 8526 remainder 0
HCF = 1

III. Find the least common multiple of the following numbers:

(i) 24, 40
24 = 2³ × 3
40 = 2³ × 5
LCM = 2³ × 3 × 5 = 120

(ii) 45, 56, 60
45 = 3² × 5
56 = 2³ × 7
60 = 2² × 3 × 5
LCM = 2³ × 3² × 5 × 7 = 2520

(iii) 207, 138
207 = 3² × 23
138 = 2 × 3 × 23
LCM = 2 × 3² × 23 = 414

(iv) 72, 96, 120
72 = 2³ × 3²
96 = 2⁵ × 3
120 = 2³ × 3 × 5
LCM = 2⁵ × 3² × 5 = 1440

(v) 120, 195, 135
120 = 2³ × 3 × 5
195 = 3 × 5 × 13
135 = 3³ × 5
LCM = 2³ × 3³ × 5 × 13 = 14040

(vi) 102, 170, 126
102 = 2 × 3 × 17
170 = 2 × 5 × 17
126 = 2 × 3² × 7
LCM = 2 × 3² × 5 × 7 × 17 = 32130