In worksheet on word problems on H.C.F. and L.C.M. we will find the greatest common factor of two or more numbers and the least common multiple of two or more numbers and their word problems.
I. Find the highest common factor and least common multiple of the following pairs of numbers:
(i) 576 and 1440
(ii) 625 and 325
(iii) 496 and 1116
(iv) 1000 and 1125
(v) 676 and 650
II. Word problems on highest common factor (H.C.F.) and lowest common multiple (L.C.M.):
(i) The product of two numbers is 120. If their H.C.F. is 6 what is their L.C.M.
(ii) Find the smallest number which, on being added 23 to it, is exactly divisible by 32, 36, 48 and 96.
(iii) Find the least length of a rope which can be cut into whole number of pieces of lengths 45 cm, 75 cm and 81 cm.
(iv) Find the greatest number of 4-digits which is exactly divisible by 40, 48 and 60.
(v) Find the greatest number of 5-digits which on being divided by 9, 12, 24 and 45 leaves 3, 6, 18 and 39 as remainders respectively.
(vi) The length, breadth, height of a room are 6m 80 cm, 5m 10 cm and 3 m 40 cm respectively. Find the longest tape which can measure the dimensions of the room exactly.
Answers for the worksheet on H.C.F. and L.C.M. are given below.
I. (i) 288; 2880
(ii) 25; 8125
(iii) 124; 4464
(iv) 135; 9000
(v) 26; 16900
II. (i) 20
(iii) 2025 cm
(vi) 1 m 70 cm