Find the least number which when divided by 12, 27 and 35 leaves 6 as a…

We are given that a number leaves remainder 6 when divided by 12, 27, and 35.

Step 1: Subtract the remainder

If the number is N, then:
N−6 is divisible by 12,27, and 35

Step 2: Find LCM of 12, 27, and 35

• 12=22×3

• 27=33

• 35=5×7

LCM=22×33×5×7= 4×27×35 =3780

Step 3: Add the remainder back

N=3780+6=3786