This topic will provide worksheet to students on H.C.F and L.C.M which will help to judge themselves their level of understanding of the topic and the areas where they need more careful study and analysis. This worksheet will serve as a yardstick for measuring the level of performance of student. The worksheet will contain H.C.F and L.C.M on various methods learnt earlier and sums on the relationship between the two.
1. Using prime factorization method find the highest common factor (H.C.F) of the following numbers:
(i) 156 and 228
(ii) 49 and 343
(iii) 56 and 65
(iv) 70 and 84
(v) 98 and 102
Answer:
(i) 12
(ii) 49
(iii) 1
(iv) 14
(v) 2
2. Using division method find the highest common factor (H.C.F) of the following numbers:
(i) 36, 28 and 48
(ii) 56, 64 and 72
(iii) 144, 200, 220
(iv) 165, 185, 210
(v) 856, 974, 1089
Answer:
(i) 4
(ii) 8
(iii) 4
(iv) 5
(v) 1
3. Using prime factorization method find the lowest common multiple (L.C.M) of the following numbers:
(i) 74, 168, 192
(ii) 85, 105, 95
(iii) 45, 50, 55
(iv) 1089, 729, 784
(v) 42, 49, 56
Answer:
(i) 49, 728
(ii) 33, 195
(iii) 4950
(iv) 69, 155, 856
(v) 1176
4. Using Division method find the lowest common multiple (L.C.M) of the following numbers:
(i) 88, 99, 121
(ii) 369, 452, 231
(iii) 45, 32, 86
(iv) 20, 30, 80
(v) 50, 100, 120
Answer:
(i) 8712
(ii) 12842676
(iii) 61920
(iv) 240
(v) 600
5. If the H.C.F and the L.C.M of two numbers are 6 and 42 respectively and one number is 21 then find the other number
Answer:
Other number is 12
6. If the two numbers are 56 and 128 then find their H. C. F and L.C. M. Verify the relationship as well H. C. F × L.C. M = Product of the two numbers.
Answer:
H.C.F = 8
L.C.M = 600
7. If the H.C.F of two numbers is 55 and the product of two numbers is 1375. Then find the L. C. M of the two numbers.
Answer:
L.C.M = 25
8. If the L.C.M of two numbers is 558 and the product of 2 numbers is 3348. Then find the H.C.F of the two numbers
Answer:
H.C.F = 6
9. Find the L.C.M and H. C. F of 108, 176 and 252 by long division method
Answer:
L.CM = 33264
H.C.F = 4
10. Find the L.C.M and H. C. F of the following by prime factorization method and verify the relationship (H. C. F × L.C. M = Product of the two numbers) in each case :
(i) 700 and 840
(ii) 960 and 580
(iii) 228 and 588
(iv) 225 and 250
(v) 850 and 1620
Answer:
(i) H.C.F = 140
L.C.M = 4200
(ii) H.C.F = 20
L.C.M = 27840
(iii) H.C.F = 12
L.C.M = 11172
(iv) H.C.F = 25
L.C.M = 2250
(v) H.C.F = 10
L.C.M = 137700
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