8. two natural numbers whose difference is 66 and the least common multiple is 360, are:

Two natural numbers whose difference is 66 and the least common multiple is 360, are:(a) 120 and 54(b) 90 and 24(c) 180 and 114(d) 130 and 64

Answer

Answer: (b) 90 and 24

35. If, LCM of two natural numbers 'x' and 'y' is 360 and their difference is 66. Then, find the value of 'x' and 'y'.

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Find two natural numbers whose difference is $$66$$ and the least common multiple is $$360$$.

Let the two numbers be $$x$$ and $$x+66$$.

Since, the LCM is 360, there must be 5,2 and 3 as the prime factors of the two numbers.

So, one pair is 24 & 90, because $$90-24=66$$.

Also, $$24=2\times2\times2\times 3$$

$$90=2\times3\times3\times 5$$

$$\therefore$$ LCM$$=2\times2\times2\times3\times3\times 5=360$$.

So, the numbers are $$24$$ and $$90$$.