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HCF AND LCM
11) A labourer was engaged for ₹5750 but paid ₹5000. What was his maximum daily wage?
Explanation
Correct Answer: ₹250
Maximum daily wage = H.C.F. of 5750 and 5000 = 250.
12) Greatest number dividing 1356, 1868 and 2764 leaving remainder 12
Explanation
Correct Answer: 64
H.C.F. of 1344, 1856 and 2752 = 64.
13) Greatest number dividing 964, 1238 and 1400 leaving remainders 41, 31 and 51
Explanation
Correct Answer: 71
H.C.F. of 923, 1207 and 1349 = 71.
14) Least number to be added to 2497 so that it is divisible by 5, 6, 4 and 3
Explanation
Correct Answer: 23
L.C.M. = 60, remainder = 37 → 60 − 37 = 23.
15) Greatest number to be subtracted from 5834 to make it divisible by 20, 28, 32 and 35
Explanation
Correct Answer: 4714
L.C.M. = 1120 → 5834 − 1120 = 4714.
16) Least number which leaves remainders 7, 10 and 11 when divided by 12, 15 and 16
Explanation
Correct Answer: 235
L.C.M. of 12, 15, 16 = 240 → 240 − 5 = 235.
17) Least number which leaves remainder 3 when divided by 5, 6, 7, 8 and is divisible by 9
Explanation
Correct Answer: 1683
Number = 840k + 3 → smallest divisible by 9 is 1683.
18) Number of trees planted if rows of 6, 8, 10, 12 leave 5 trees and rows of 13 leave none
Explanation
Correct Answer: 845
Number = 120k + 5 → smallest divisible by 13 is 845.
19) Two devices beep every 60 sec and 62 sec. Next together time after 10 a.m.
Explanation
Correct Answer: 10.31 a.m.
L.C.M. of 60 and 62 = 1860 sec = 31 min.
20) Six bells ring at intervals of 2, 4, 6, 8, 10 and 12 seconds. How many times together in 30 minutes?
Explanation
Correct Answer: 16
L.C.M. = 120 sec = 2 min → (30 ÷ 2) + 1 = 16 times.
