Question

IS 111,
15. Can two numbers have 15 as HCF and 350 as LCM? Why?​

Answer 1

Answer:

No ,2 numbers cannot have HCF as 15 and LCM as 350 . Because LCM>HCF and HCF of 2 numbers should divide the LCM completely.

Step-by-step explanation:

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Answer 2

The LCM (Least Common Multiple) of two numbers must be a Multiple of the HCF (Highest Common Factor) of those numbers. It’s in the name.

Is 350 a multiple of 15?

No, 350 ÷ 15 = 23 with a remainder of 5, so 350 is not a multiple of 15

Alternate Answer:

The HCF (Highest Common Factor) of two number must be a factor of any multiple of either of those numbers, including the Least Common Multiple. It’s in the name.

If the Highest Common Factor is 15

then any multiple must be equal to: n × 15

Is 15 a factor of 350?

No, the factors of 350 are 2 × 5² × 7, so 350 is not divisible by 15 or by 3.

We could have figured out that 15 is not a factor by using the tricks for checking divisibility.

3 + 5 + 0 = 8

8 is not divisible by 3, so 350 is not divisible by 3

Since 350 is not divisible by 3, 350 is not divisible by 15, the HCF.