Find two natural numbers whose difference is 66 LCMis 360 - Maths - Real Numbers

Question

Find two natural numbers whose difference is 66 & LCMis
360

Ajanta Trivedi · Accepted Answer

let the numbers are a and b where $a, b > 0$ such that their LCM = 360 = $2^{3} * 3^{2} * 5$ and their difference = 66 therefore $a - b = 66 \Rightarrow a = b + 66$ here a is greater than 66 and LCM = 360 if a = 120 , b = 120-66 = 54 since $54 = 2 * 3^{3}$ thus the LCM of 120 and 54 is not 360 if a = 90 , b = 90-66 = 24 since $24 = 2^{3} * 3$ thus the LCM of 90 and 24 is 360 and their difference = 66 thus 90 and 24 are the required numbers hope this helps you cheers!!

Find two natural numbers whose difference is 66 & LCMis 360.