LCM and HCF MCQs Read Discuss Courses LCM and HCF Factors and Multiples : All the numbers that divide a number completely, i.e., without leaving any remainder, are called factors of that number. For example, 24 is completely divisible by 1, 2, 3, 4, 6, 8, 12, 24. Each of these numbers is called a factor of 24 and 24 is called a multiple of each of these numbers … More on LCM and HCF LCM Please wait while the activity loads. If this activity does not load, try refreshing your browser. Also, this page requires javascript. Please visit using a browser with javascript enabled. If loading fails, click here to try again Question 1Three friends started running together on a circular track at 8:00:00 am. Time taken by them to complete one round of the track is 15 min, 20 min, 30 min respectively. If they run continuously without any halts, then at what time will they meet again at the starting point for the fourth time ?8:30:00 am9:00:00 pm12:00:00 pm12:00:00 amLCM Numbers Discuss itQuestion 1-Explanation: LCM (15, 20, 30) = 60 => They meet at the starting point after every 60 min, i.e., after every 1 hour. Therefore, they will meet at the starting point for the fourth time after 4 hours, i.e., at 12:00:00 pm.Question 2The LCM of two co-prime numbers is 117. What is the sum of squares of the numbers ?220153025022LCM Numbers Discuss itQuestion 2-Explanation: 117 = 3 x 3 x 13 As the numbers are co-prime, HCF = 1. So, the numbers have to be 9 and 13. 92 = 81 132 = 169 Therefore, required answer = 250Question 3HCF of two numbers is 11 and their LCM is 385. If the numbers do not differ by more than 50, what is the sum of the two numbers ?132351236Numbers LCM HCF Discuss itQuestion 3-Explanation: Product of numbers = LCM x HCF = 11 x 385 = 4235 Let the numbers be of the form 11m and 11n, such that 'm' and 'n' are co-primes. => 11m x 11n = 4235 => m x n = 35 => (m,n) can be either of (1, 35), (35, 1), (5, 7), (7, 5). => The numbers can be (11, 385), (385, 11), (55, 77), (77, 55). But it is given that the numbers cannot differ by more than 50. Hence, the numbers are 55 and 77. Therefore, sum of the two numbers = 55 + 77 = 132Question 4Two numbers are in the ratio of 5:7. If their LCM is 105, what is the difference between their squares ?21621072840Numbers LCM HCF Discuss itQuestion 4-Explanation: Let 'h' be the HCF of the two numbers. => The numbers are 5h and 7h. We know that Product of Numbers = LCM x HCF => 5h x 7h = 105 x h => h = 3 So, the numbers are 15 and 21. Therefore, difference of their squares = 212 - 152 = 441 - 225 = 216Question 5Which of the following is the largest of all ? (i) 7/8 (ii) 15/16 (iii) 23/24 (iv) 31/32(i)(ii)(iii)(iv)Numbers LCM Number Divisibility Discuss itQuestion 5-Explanation: LCM (8, 16, 24, 32) = 96 7/8 = 84/96 15/16 = 90/96 23/24 = 92/96 31/32 = 93/96 Hence, 31/32 is the largest of all.Question 6Two numbers are in the ratio 3 : 5. If their L.C.M. is 75. what is sum of the numbers?25454050LCM Discuss itQuestion 6-Explanation: 1st number = 3x 2nd number =5x LCM of 3x and 5x is 15x => 15x = 75 => x = 5 sum = 15+25 =40 Question 7Ratio of two numbers is 3:2. If LCM of numbers is 60, then smaller number is?20304050LCM Discuss itQuestion 7-Explanation: say, 1st number =3x 2nd number =2x LCM of numbers = 6x given LCM = 60 => x6 = 60 =>x = 10 Question 8Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 240. Their H.C.F. is:40203010LCM Discuss itQuestion 8-Explanation: Let the numbers be 2x, 3x and 4x LCM = 12x 12x=240 ⇒x=20 H.C.F of 40, 60 and 80=20Question 9What is the lowest common multiple of 12, 36 and 20?120180360240LCM Discuss itQuestion 9-Explanation: LCM = 180Question 10What is the least number which when divided by 4, 5, 6 and 7 leaves a remainder 3, but when divided by 9 leaves no remainder?16831263843423LCM Discuss itQuestion 10-Explanation: LCM of 4,5,6,7 is 420 =>(420k+3) should be divisible by 9 if k =1, 423/9 remainder !=0 12 There are 16 questions to complete. You have completed questions question Your accuracy is Correct Wrong Partial-Credit You have not finished your quiz. If you leave this page, your progress will be lost. Correct Answer You Selected Not Attempted Final Score on Quiz Attempted Questions Correct Attempted Questions Wrong Questions Not Attempted Total Questions on Quiz Question Details Results Date Score Hint Time allowed minutes seconds Time used Answer Choice(s) Selected Question Text All doneNeed more practice!Keep trying!Not bad!Good work!Perfect! Last Updated : 03 Oct, 2023