Question

Consider that two number whose sum is 135 and their HCF is 27 if their LCM is 162 then what will be the larger number?

Answer 1

Step-by-step explanation:

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Answer 2

let the two number be a and b

so,

$a + b = 135 \\ hcf = 27 \\ so \: each \: one \: is \: divisible \: by \: 27 \\ 27x + 27y = 135 \\ so$

the possible value for x and y are (1,4),(2,3)

HCF means that the both number are divisible by 27 so we have written a as 27x and b as 27y hair the value of x and y are written but we need to find the value of a and b

by putting the value of x and y as 1,4

a=27x=1×27=27

b=27x=4×27=108

lcm =108

not possible because the lcm of a and b is 162

X and y as 2 and 3

a=27x=27×2=54

b=27x=27×3=108

lcm= 162

the value of x and y are 2 and 3 and the value of a and b are 54 and 108