Problems on H.C.F and L.C.M
A heap of stones can be made up into groups of 21. When made up into groups of 16, 20, 25 and 45 there are 3 stones left in each case. How many stones at least can there be in the heap?
The least number which when divided by 4,5,6,8 and 10 is the LCM of these numbers. But each time to get 3 as remainder, we have to add the remainder 3 to the obtained LCM.LCM of (4, 5, 6, 8, 10)+ 3=120+3=123
The largest 4 digit number is 9999.We know that , if LCM of given numbers divide a number N , then N is exactly divisible by all the given numbers .LCM of 12,15,18,27 is 540.On dividing 9999 by 540 we get 279 as remainder.Therefore number =9999 - 279 =9720.
To solve this question quickly, first remove decimal by multiplying each term with 100,Then terms become 210, 105, 63Then HCF of above terms is 21, So Answer is 0.21
EXAMIANS