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 6^{th} day. Andy goes to the same shopping mall every 7^{th} day. How many times will they meet in the mall in the month of December and January if we start counting from 1^{st} 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 2^{nd} day and painting class every 3^{rd} 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.
(xix) Three bells ring at intervals of 8, 15 and 16 seconds respectively. At what time will they ring together if they start ringing at 10 a.m?
(xx) Find the largest number which divides 1131, 1218 and 1389 leaving remainders 6, 3 and 9 respectively.
(xxi) Find the largest number which is the factor of 2075, 3320 and 4565.
(xxii) Find the least 5-digit number which leaves remainder 2 in each case when divided by 3, 6, 9, 12, 15, 18 and 27.
(xxiii) Find the least natural number which when divided by 16, 36 and 90 leaves a remainder 13.
(xxiv) Find the number nearest to 999 but greater than 999, which is exactly divisible by 6, 12 and 18.
(xxv) Find the largest number that will divide 168, 234 and 366 leaving a remainder 3 in each case.
(xxvi) Find the number nearest to 1000 but greater than 1000, which is exactly divisible by 15, 20 and 25.
(xxvii) Find the greatest 4-digit number which when divided by 18, 24, 30 and 36 leaves a remainder 15 in each case.
(xxviii) Find the least natural number which when divided by 688 and 1248 leaves a remainder 2.
(xxix) Find the largest number which divides 2039, 2499 and 2957 leaving remainders 5, 13 and 19 respectively.
(xxx) Find the largest number which divides 42 and 96 leaving remainders 3 and 5 respectively.
(xxxi) Find the largest number which when divided by 3124 and 4099 leaves a remainder 4 in each case.
Answers for the worksheet on H.C.F. and L.C.M. are given below.
Answers:
I. (i) 288; 2880
(ii) 25; 8125
(iii) 124; 4464
(iv) 135; 9000
(v) 26; 16900
II. (i) 20
(ii) 265
(iii) 2025 cm
(iv) 9840
(v) 120
(vi) 42
(vii) 24
(viii) 3
(ix) 150, 165, 180, 195
(x) 1
(xi) 90
(xii) 99714
(xiii) 1 m 70 cm
(xiv) 20
(xv) 6
(xvi) 350
(xvii) 480
(xviii) 4
(xix) 10:04 a.m.
(xx) 15
(xxi) 415
(xxii) 10262
(xxiii) 733
(xxiv) 1008
(xxv) 33
(xxvi) 1200
(xxvii) 9735
(xxviii) 53666
(xxix) 226
(xxx) 13
(xxxi) 195
Common Multiples.
Least Common Multiple (L.C.M).
To find Least Common Multiple by using Prime Factorization Method.
Examples to find Least Common Multiple by using Prime Factorization Method.
To Find Lowest Common Multiple by using Division Method
Examples to find Least Common Multiple of two numbers by using Division Method
Examples to find Least Common Multiple of three numbers by using Division Method
Relationship between H.C.F. and L.C.M.
Worksheet on H.C.F. and L.C.M.
Word problems on H.C.F. and L.C.M.
Worksheet on word problems on H.C.F. and L.C.M.
5th Grade Math Problems
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