Question

Find the smallest 4-digitnumber that is divisible by 30 & 45.

Answer 1

30’s prime factors: 2*3*5

45’s prime factors: 3*3*5

So we need at least one two, two threes, and one five.

The LCM of 30 and 45 is 90.

1000 is the lowest four digit number

1000/90=11r10

90–10=80

So 1080 will be evenly divisible by 90, and thus by both 30 and 45

1080/90=12

1080/45=24

1080/30=36

Answer 2

Step-by-step explanation:

The smallest 4-digit =1000

Now L.C.M of 12,15,20and35

2∣12,15,20,35

2∣6,15,20,35

3∣15,5,35

5∣1,5,5,35

7∣1,1,1,1

1,1,1,1

L.C.M.=2×2×3×5×7=420

We divided 1000 by 420

420)1000(2

−840

160−Remainder

∴ The least 4−digit number that is exactly divisible by 12,15,20 and 35

=1000+(420−160)

=1000+260=1,260

hope it help