Question

If x is prime, y is a composite number such that x + y = 240 and their LCM is 4199. Find x and y.

Answer 1

We know that the LCM of a prime number and a composite number is equal to their product.
So, xy = 4199
Now, x + y = 240
⇒ y = 240 − x
Substituting the value of y in xy = 4199, we will get
x( 240 − x) = 4199
⇒ 240x − x² = 4199
⇒ x² − 240x + 4199 = 0
⇒ x² − 19x − 221x + 4199 = 0
⇒x(x − 19) − 221(x − 19) = 0
⇒ (x − 19)(x − 221) = 0
⇒ (x − 19) = 0 or (x − 221) = 0
⇒ x = 19, 221
∴ x = 19 and y = 221 or x = 221 and y = 19