Question

What is the largest possible length of a scale that can be used to measure exactly the lengths 3m, 5m 10 cm,12m 90cm?

Answer 1

This tests the concept of GCD.

We will first convert the lengths to be in the Same units :

3 × 100 = 300cm

5 × 100 = 500cm

12 × 100 = 1200

We want the GCD of :

300 cm, 510 cm, 1290 cm

300 = 2 × 2 × 3 × 5 × 5

510 = 2 × 3 × 5 × 17

1290 = 2 × 3 × 5 × 43

The common factors in both is :

2 × 3 = 6

The answer is 6cm

Answer 2

Answer:

30 cm

Step-by-step explanation:

First lets convert it into the same unit i.e. cm

3m = 300cm

5m 10cm = 510cm

12m 90cm = 1290cm

So the possible length (greatest) would be the H.C.F of the terms

300 = 2x2x3x5x5

510 = 2x3x5x17

1290 = 2x3x5x43

So the highest common factor is :

2x3x5

=6x5

=30cm

I hope you like my answer.