Multiple Choice Questions

Three numbers are in the ratio 3 5 7 and their LCM is 840 Their HCF is ........

Quantitative Aptitude (MTS) LCM, HCF

Three numbers are in the ratio 3 : 5 : 7 and their LCM is 840. Their HCF is:

This questions was previously asked in

SSC MTS 13th October 2021 Shift-3

- Let's denote the numbers by 3x, 5x, and 7x.

- Their LCM is given as 840.

- The LCM of 3x, 5x, 7x is the product of the highest powers of all unique prime factors in the numbers.

- The LCM can also be found by the formula LCM = (Product of numbers) / HCF.

- The product of numbers is (3x) * (5x) * (7x) = 105x³.

- So, 105x³ / HCF = 840.

- The integer solutions for x that make the LCM 840 are few and testing them, you find x = 4.

- Substitute x = 4: numbers become 12, 20, and 28.

- HCF of 12, 20, and 28 is 4.

The correct answer is Option: 1, 4.

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