Question

Shortcut tricks to find hcf and lcm of any number with example buying in english

Answer 1

Hi friend

How are you?

Here is your answer:-

ANSWER:-

Tips and Tricks:

1) H.C.F. and L.C.M. of Fractions

a) H.C.F. = H.C.F. of Numerator

L.C.M. of Denominator

Example

H.C.F. of l , m , n = H.C.F. of (l, m, n)

a b c L.C.M. of (a, b, c)

b) L.C.M. = L.C.M. of Numerator

H.C.F. of Denominator

L.C.M. of l , m , n = L.C.M. of (l, m, n)

a b c H.C.F. of (a, b, c)

2) Product of two numbers = Product of their H.C.F. and L.C.M.

This condition is only true for two given numbers. If H.C.F. and L.C.M. of three or more numbers are given, then this rule is not applicable.

3) H.C.F. and L.C.M. of decimal fractions: To find H.C.F. or L.C.M. of 0.5, 1.6, etc, consider these numbers without decimal point i.e 5, 16 and solve using normal methods used to determine H.C.F. or L.C.M.. In the result, mark off as many decimal places as there are in each of the given number.

4) Comparison of fractions: Find L.C.M. of denominators of given fractions. Convert each fraction into equivalent fraction with L.C.M. as denominator, by multiplying both numerator and denominator by same number. The resultant fraction with the greatest numerator is greatest.

Question Variety:

Generally 5 types of questions are asked in this chapter. Understanding and studying these concepts will in solving this chapter as well as help in solving some topics in other chapters.

I hope this answer may help you.

Thank you,

Goodbye and have a nice day.

Answer 2

Answer:

Step 1 :

We have to decompose the given numbers in to prime factors.

In the example shown above, we have the two numbers 24 and 60.

24 = 2 x 2 x 2 x 3

60 = 2 x 2 x 3 x 5

Step 2 :

Now, we have to draw two circles as shown above. The first one is for 24 and the second one is for 60.

Step 3 :

In the prime factors of 24 and 60, strikeout the common factor (which is found in both 24 and 60) and write that one in common region (intersection part) of two circles.

Step 4 :

If we find a prime factor which is in 24 but not in 60, strikeout that one and it has to be written in the circle of 24 (not in the common region).

If we find a prime factor which is in 60 but not in 24, strike out that one and it has to be written in the circle of 60 (not in the common region).

This process has to be continued until all the prime factors of both 24 and 60 are struck out.

Step 5 :

Once all the prime factors of both 24 and 60 are struck out, we have to do the following works to get HCF and LCM.

H.C.F = Multiply the prime factors which are found in the common region (Intersection part).

So, the H.C.F of 24 and 60 is

= 2 x 2 x 3

= 12

L.C.M = Multiply all the prime factors which are found in the two circles (Including the prime factors in the common region)

So, the L.C.M of 24 and 60 is

= 2 x 2 x 2 x 3 x 5

= 120