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There are two containers A and B of capacity 45 kg and ‘x’ kg respectively. A container of largest measure of 15 kg can measure containers A and B exactly while a container Q of smallest measure of ‘2x + 60’ kg can be measured by containers A and B exactly, then what is the LCM of ‘x + 15’ and ‘2x – 15’?

There are two containers A and B of capacity 45 kg and ‘x’ kg respectively. A container of largest measure of 15 kg can measure containers A and B exactly while a container Q of smallest measure of ‘2x + 60’ kg can be measured by containers A and B exactly, then what is the LCM of ‘x + 15’ and ‘2x – 15’? Correct Answer 525

Formula Used:

First number × Second number = HCF × LCM

Calculation:

Capacity of container of largest measure that can measure A and B exactly = HCF of capacity of A and B = 15 kg

Capacity of container of smallest measure that can be measured A and B exactly = LCM of capacity of A and B = (2x + 60) kg

⇒ 45 × x = 15 × (2x + 60)

⇒ 3x = 2x + 60

⇒ x = 60

∴ LCM of ‘x + 15’ and ‘2x – 15’  = LCM of 75 and 105

= 525

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