Question
Find the least 4-digit number which, when divided by 9,
12, and 15, leaves a remainder of 4 in each case.Solution
Prime factorization of 9 = 3²
Prime factorization of 12 = 2² × 3
Prime factorization of 15 = 3 × 5 LCM of (9, 12, and 15) = 2² × 3² × 5 = 180 Least 4-digit number divisible by 180 = 1,080 So, required number = 1080 + 4 = 1,084 Hence, option A.
Determine the smallest four-digit number that is evenly divisible by 12, 22, and 42.
Three natural numbers X,Y,Z are pairwise co-prime and satisfy the following conditions, the least common multiple (LCM) of X and ...
The smallest natural number that must be added to 1212 to make it a perfect square is:
There are three numbers 'u', 'v' and 'w' (u < v < w) such that 'v' is equal to the average of 'u' and 'w'. 80% of 'w' is equal to 'u' and the difference...
If 893x2 is divisible by 56, and x > 6, find x.
Consider three numbers whose total is 294. The first and second numbers are in a ratio of 5:7, and the second and third numbers are in a ratio of 7:9. D...
- If 246x179y is divisible by 72, find the value of (x + 2y).
Find the sum of the first 30 natural numbers.
A number is initially increased by 37.5% and then reduced by 40%. The final value obtained after these changes is 6,270. Determine 80% of the original n...
Relevant for Exams:
