Question

LCM of two numbers is 1134 and HCF is 18. if one of the numbers is 162, find the other. number.​

Answer 1

Answer:  126

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Work Shown:

Let x and y be the two numbers.

We're given x = 162 and the variable y is unknown.

We're also given LCM = 1134 and HCF = 18

So,

LCM = (x*y)/HCF

1134 = 162*y/18

1134 = (162/18)y

1134 = 9y

9y = 1134

y = 1134/9

y = 126

The other number is 126

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Notice that

• 162 = 18*9
• 126 = 18*7

showing that 18 is the highest common factor (HCF) of the numbers 162 and 126. This partially confirms the answer.

Now let,

• A = multiples of 162
• B = multiples of 126

So,

• A = 162, 324, 486, 648, 810, 972, 1134, 1296, ...
• B = 126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260, ...

We see that 1134 is in each list of multiples and the smallest such common item. So the lowest common multiple (LCM) of 162 and 126 is 1134. This helps fully confirm the answer.