Question

can two numbers have 22 as their hcf and 143 as their LCM?if not why​

Answer 1

lcm(a,b)=a×bhcf(a,b) so here the two numbers must have a product of 143×22=3,146 and be both divisible by 22. Now the divisors of 3,146 are: 1, 2, 11, 13, 22, 26, 121, 143, 242, 286, 1,573 and 3,146. The multiples of 22 in this list are 22, 242, 286 and 3,146.

So there are 2 integer pairs that make this true:

22 and 3,146

242 and 286.

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Answer 2

Answer:

No

Explanation 1:

The two numbers must be 22a and 22b, where a and b must be relatively prime. But the two numbers must both divide 143. Since 143 is not divisible by 22, there cannot be two such numbers.

Explanation 2:

Let the two numbers be 22a & 22b where a&b are coprimes.

=> 22a x 22b = 22 x 143

=> ab = 143/22

=> a & b are not both integers

=> Such pair of numbers does not exist.

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