How to check if LCM is to be found or HCF

When to use LCM or HCF?

Generally,

When we have to find a number larger than given numbers,

then we find LCM.

If we have to find smaller number,

then we find HCF .

Let’s take some examples

Find the least number which when divided by 6, 15 and 18 leave remainder 5 in each case

In this case,

We have to find a number which needs to be divided by 6, 15, 18

So, it will be bigger than 6, 15, 18

∴ We find LCM

Check the solution here – Ex 3.7, 8

Two tankers contain 850 liters and 680 liters of kerosene oil respectively. Find the maximum capacity of a container which can measure the kerosene oil of both the tankers when used an exact number of times.

Assume that we have two buckets of 850 and 680 litres,

and we need to find a mug.

So, the container size will be smaller than both the tanks size

Thus, we have to find a smaller number than 850 and 680.

So, we find HCF

Check the solution here – Example 12

In a morning walk, three persons step off together. Their steps measure 80 cm, 85 cm and 90 cm respectively. What is the minimum distance each should walk so that all can cover the same distance in complete steps?

Here, the distance they should walk will be bigger than  80, 85, 90

So, we have to find a larger number

Thus, we find LCM

Check the solution here – Example 13

Renu purchases two bags of fertilizer of weights 75 kg and 69 kg. Find the maximum value of weight which can measure the weight of the fertilizer exact number of times.

Here, we are measuring weights

So, the measuring weight will be smaller than the two given weights

∴ We use HCF

Check the solution here – Ex 3.7, 1