2023 · Q32
If x is the smallest natural number that is divisible by both 24 and 30, whereas y is the largest natural number that divides both 36 and 100, then what is the value of x – y?
General Mental Ability, Quantitative Aptitude and StatisticsNumber system and arithmetic
- A116
- B124
- C132
- D138
Explanation
The smallest natural number divisible by both 24 and 30 is their LCM: 24 = 2^3 x 3 and 30 = 2 x 3 x 5, so LCM = 2^3 x 3 x 5 = 120, giving x = 120. The largest natural number dividing both 36 and 100 is their GCD: 36 = 2^2 x 3^2 and 100 = 2^2 x 5^2, so GCD = 2^2 = 4, giving y = 4. Therefore x - y = 120 - 4 = 116, option (a).