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) What is the least number of saplings that can be arranged in rows of 12, 15 or 40 in each row?
(vi) 210 oranges, 252 apples and 294 pears are equally packed in cartons so that no fruit is left. What is the biggest possible number of cartons needed?
(vii) A certain number of students can be arranged in groups of 3, 4, 6 or 8 with no student left behind. Find the number of students.
(viii) The local bus service has 2 lines of buses that start together at 8 a.m. Buses on line A leave after every 15 minutes while Buses on line B leave after every 20 minutes. In a day, how many times do buses on both line A and B leave together between 8 a.m. and 11 a.m.
(ix) Three painters Ron, Victor and Shelly are painting the rooms of a hotel which are numbered from 15 – 200. Ron has to work in all the rooms. Victor has to work in rooms where the room number is a multiple of 3. Shelly has to work in rooms where the room number is a multiple of 5. In which rooms will they all work together?
(x) Sara goes to the shopping mall every 6th day. Andy goes to the same shopping mall every 7th day. How many times will they meet in the mall in the month of December and January if we start counting from 1st December?
(xi) The HCF of two numbers is 6, if one of the numbers is 42, find the other number?
(xii) 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.
(xiii) The length, breadth, height of a room are 6 m 80 cm, 5 m 10 cm and 3 m 40 cm respectively. Find the longest tape which can measure the dimensions of the room exactly.
(xiv) Sam can jump 4 steps at a time and Nina can jump 5 steps at a time. On which of the steps will both meet if both start jumping together?
(xv) Mary has a dance class every 2nd day and painting class every 3rd day. On which of the day will she have both the classes?
(xvi) Find a multiple of 70 which is between 200 and 600 which has odd digits at tens and hundreds place.
(xvii) Find a multiple of 120 which lies between 400 and 500 where the digit at tens place is double the digit at hundreds place.
(xviii) Shane wants to plant 28 marigold plants and 36 rose plants in his garden. What is the greatest number of rows possible if each row has the same number of marigold plants and the same number of rose plants.
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
(ix) 150, 165, 180, 195
(xiii) 1 m 70 cm