breaks at 10. a) 8 and 10 are any two given numbers. Answer the following questions. (i) Find the H.C.E and L.C.M. of 8 and 10. (ii) Find the product of their H.C.F. and L.C.M. (iii) Show that the product of 8 and 10 is equal to the product of their H.C.E and L.C.M.

The HCF of two numbers is the highest number that divides both numbers evenly i.e. without a remainder
We can find the HCF as follows
Factor both numbers
8 = 2 x 2 x 2
10 = 2 x 5

Find the common factor that occurs in both the least number of times

Looking at the factors we see that only 2 appears in both. So 2 is the highest common factor or HCF

LCM
Least common multiple is the lowest number that can be divided by both numbers without a remainder

Find multiples of each number and choose the lowest multiple that is common to both

Multiples of 8: 8, 16, 24, 32, 40, 48, ....
Multiples of 10: 10, 20, 30, 40, 50, ....

We see that 40 is the least common multiple

So HCF = 2

LCM = 40

HCF x LCM = 2 x 40 = 80

This is the same as the product of the two numbers 8 and 10 since 8 x 10 = 80

So HCF x LCM = product of the numbers

breaks at 10. a) 8 and 10 are any two given numbers. Answer the following questions. (i) Find the H.C.E and L.C.M. of 8 and 10. (ii) Find the product of their H.C.F. and L.C.M. (iii) Show that the product of 8 and 10 is equal to the product of their H.C.E and L.C.M. ​

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breaks at 10. a) 8 and 10 are any two given numbers. Answer the following questions. (i) Find the H.C.E and L.C.M. of 8 and 10. (ii) Find the product of their H.C.F. and L.C.M. (iii) Show that the product of 8 and 10 is equal to the product of their H.C.E and L.C.M.