HCF and LCM Questions & Answers with Notes
Find the HCF of 84, 126, and 210.
The LCM of two numbers is 180 and their HCF is 15. If one number is 45, find the other number.
Three bells ring at intervals of 12 minutes, 18 minutes, and 20 minutes respectively. If they all ring together at 9:00 AM, when will they next ring together?
Find the smallest number which when divided by 15, 20, and 35 leaves remainder 7 in each case.
The HCF of two numbers is 16 and their product is 3584. Find their LCM.
Find the greatest number that divides 285, 333, and 399, leaving remainders 9, 9, and 3 respectively.
Two numbers are in the ratio 3:4. If their LCM is 84, find their HCF.
A rectangular field is 180 m long and 105 m wide. Square plots of equal size are to be marked. Find the side length of the largest possible square plot.
Find the LCM of 72, 108, and 180.
The sum of two numbers is 45 and their HCF is 9. How many such pairs are possible?
Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, and 12 seconds. In 30 minutes, how many times do they toll together?
Find the smallest number greater than 1000 that is divisible by each of 12, 15, 18, and 20.
The HCF and LCM of two numbers are 15 and 300 respectively. If one number is 60, find the other number.
Find the number of pairs of positive integers whose HCF is 12 and LCM is 144.
A trader wants to pack 195 apples, 156 oranges, and 234 bananas into boxes such that each box contains the same number of each fruit. What is the maximum number of boxes he can pack?
Two runners start at the same point and run around a circular track. One completes a lap in 6 minutes, the other in 10 minutes. After how many minutes will they meet again at the starting point?
Find the smallest 4-digit number which is exactly divisible by 15, 20, and 35.
If HCF(a,b) = 18 and a + b = 126, and their product is 3240, find the values of a and b.
A number when divided by 391 gives remainder 47. What remainder will it give when divided by 17?
Find the largest number which divides 245 and 1029 leaving remainders 5 and 9 respectively.
Find the LCM of 84, 90, and 120.
The product of HCF and LCM of two numbers is 2160. If their HCF is 12, find their LCM.
Find the HCF of 24 × 32 × 5, 23 × 33 × 7, and 25 × 3 × 52.
A rectangular courtyard 18 m long and 12 m wide is to be paved with square tiles of the same size. What is the least number of square tiles required?
If the ratio of two numbers is 4:9 and their HCF is 7, what is their LCM?
The LCM of three numbers is 1260. Two of the numbers are 35 and 45. What could be the third number?
Find the smallest number which when increased by 1 is exactly divisible by 12, 16, 18, and 21.
Two numbers are such that their product is 504 and their HCF is 6. How many such pairs exist?
A rectangular garden 24 m × 32 m is to be divided into square plots of equal size. If the plots should be as large as possible, how many plots will there be?
The HCF of two numbers is one-fourth of their LCM. If their product is 432, find their HCF.