Subject
Quantitative Aptitude
Topic
Number
What is the least number which when divided by 52 leaves a remainder of 33, when divided by 78 leaves a remainder of 59 and when divided by 117 leaves a remainder of 98?
What is the least number which when divided by 52 leaves a remainder of 33, when divided by 78 leaves a remainder of 59 and when divided by 117 leaves a remainder of 98?
ক)
449খ)
454গ)
468ঘ)
426ঙ)
487Explanation
If we carefully observe all the cases we find, 52 – 33 = 19 78 – 59 = 19 117 – 98 = 19 In every case, the remainder is less than the divisor by 19. Thus, if we add 19 to the required number then it will be exactly divisible by 52, 78 and 117. ∴we can conclude that the required number is 19 less than the LCM of 52, 78 and 117. 52 = 2 × 2 × 13 78 = 2 × 3 × 13 117 = 3 × 3 × 13 ∴ LCM of 52, 78, 117 = (2 × 2 × 3 × 3 × 13) = 468 The required number is 19 less than the LCM of 52, 78, 117. ∴the required number = 468 – 19 = 449Related questions
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