Question

If a number is divisible by 3 and 5, then the number is always divisible by:
a) All the multiples of 3
b) All the multiples of 5
c) All the multiples of 15
d) Only 15​

Answer 1

Answer:

d) only 15

Step-by-step explanation:

A number is divisible by 3 when the sum of the absolute values of its numbers is a multiple of 3.

Example, the number 12 is divisible by 3 because the sum of 1 + 2 is multiplied by 3

A number is divisible by 5 when it ends in zero or five.

The number 10 is divisible by 5 because it ends in ZERO

The number 15 is divisible by 3 and by 5

The number 15 is divisible by 3 since 1 + 5 = 6 and 6 is a multiple of 3

The number 15 is divisible by 5 since it ends in 5

Answer 2

If a number is divisible by 3 and 5, then the number is always divisible by Only 15​

"If Any number is divisible by two numbers a and b then number is always

divisible by LCM ( a , b)"

LCM  - Least common multiplier of given numbers is the least number which is perfectly divisible by given numbers.

LCM = product of each factor  of highest power

Given that Number if Divisible by both 3 and 5

3 and 6 are prime numbers

Hence LCM ( 3 , 5 ) = 15

Hence , Number if always divisible by 15

Lets check other options

with an example

Number 45 is divisible by  3 and 5  as well as 15

Number 45 is not divisible by 60  where 60 is a multiple of 3 as well multiple of 5 and 15

Hence option a , b and c are not correct

So correct option is d) only 15

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