Question

find the smallest number which is when divided by 25 30 and 75 LCM​

Answer 1

Answer:

We first need to find the LCM of 12,20,30 and 60.

To find LCM, we first write all numbers as products of their prime numbers.

12=2×2×3

=2

2

×3

1

20=2×2×5

=2

2

×5

1

30=2×3×5

=2

1

×3

1

×5

1

60=2×2×3×5

=2

2

×3

1

×5

1

We then choose each prime number with the greatest power and multiply them to get the LCM.

LCM

=2×2×3×5

=4×3×5

=60

Hence, 60 is the smallest number which is exactly divisible by 12,20,30 or 60

So, the smallest number which when divided by 12,20,30 or 60 leaves a remainder 5 each time will be 60+5=65.

Answer 2

⇒25=5×5

⇒30=2×3×5

LCM(25,30)= Product of greatest of each factor of the given numbers

=->2×3×5×5 = 150

Now the required number is 150+5 = 155 Ans.