# L.C.M and H.C.F.

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## Practice Questions on LCM and HCF

 Q20) Find the least number which when increased by 5 is divisible by 12 and 16. 1) 912) 433) 534) 21 Let N be the required number. N + 5 = L.C.M.(12,16) N + 5 = 48 i.e. N = 43 Hence, option 2. Q21) What is the minimum number of square marble slabs requires to tile a floor of length 5 meters 78 cm and width 3 meters 74 cm. 1) 1762) 683) 5404) 187 Side of the square marble slab is H.C.F(578,374) = 34 Total number of slabs required = Hence, option 4. Q22) Let 'A' denote a set of positive integers, each of which when divided by 12 and 16 leaves 3 as the remainder. How many of the numbers in 'A' are between 0 and 250? 1) 32) 63) 14) 5 Required numbers are of the form (L.C.M.(12,16))k + 3 = 48k + 3 Therefore, required numbers are 51, 99, 147, 195, 243 Hence, option 4. Q23) For two positive integers a and b defined is the function h(a,b) as the HCF of a,b. Let A be a set of n positive integers, G(A), the HCF of elements of A is computed by repeatedly using the function h. The minimum number of times h is required to be used to compute G is 1) n + 12) n - 13) (n + 1)/24) n To find the H.C.F. of n numbers we have to use the function n - 1 times Hence, option 2. Q24) Find the least number which when divided by 24, 32 and 36 leaves the remainders 19, 27 and 31 respectively. 1) 2832) 2933) 5714) 581 Note: Here 24 – 19 = 5, 32 – 27 = 5, 36 – 31 = 5 Required number = LCM(24, 32, 36) – 5 = 283 Hence, option 1. Q25) Find the least number which when divided by 24, 30 and 54 leaves 5 as remainder in each case. 1) 10802) 10753) 10704) 1085 Required number = LCM(24, 30, 54) + 5 = 1085 Hence, option 4.