CBSE Class 10 Answered

For this it is required to remember what HCF and LCM are and then it is required to analyse the given numerical.

If a greatest number divides the numbers a, b and c, then in that case the greatest number is the HCF of these three numbers.

If a smallest number is multiple of the numbers a, b and c, then in that case the least number is the LCM of these three numbers.

Consider a numerical as follows:

3 strings of different lengths, 240 cm, 318 cm and 426 cm are to be cut into equal lengths. What is the greatest possible length of each piece?

As per the given information it is required to find the greatest length of each piece of string. From this it is clear that these greatest lengths of strings divide the lengths 240 cm, 318 cm and 426 cm.

Clearly, the greatest length of each piece of strings is the HCF of 240 cm, 318 cm and 426 cm.

Consider another numerical as follows:

Two lighthouses flash their lights every 20s and 30s respectively. Given that they flashed together at 7pm, when will they next flash together?

As per the given information it is required to find the least time taken by the light houses to flash their lights.

Clearly this least time is a least multiple of 20s and 36s and this can be found by taking their LCM.