HCF and LCM sums tips and tricks (Part-2)



HCF and LCM sums tips and tricks


Start solving the critical sums in an easy way using HCF and LCM formula!!

Introduction

HCF is defined as the Highest Common Factor and LCM is Least Common Multiple. HCF and LCM sums are very useful in solving mathematical problems. This helps in solving the sums quickly and saves time. Aspirants preparing for competitive exams must learn HCF and LCM sums so that they can save time and complete their exams on time with the correct answers. Learn HCF and LCM with question and answer!!

Formulas to use :

1. Factors and Multiples:

If a number a divided by another number b exactly, we say that a is a factor of b.

In this case, b is called a multiple of a.

2. Highest Common Factor (H.C.F.) or Greatest Common Measure (G.C.M.) or Greatest Common Divisor (G.C.D.):

The H.C.F. of two or more than two numbers is the greatest number that divides each of them exactly.

There are two methods of finding the H.C.F. of a given set of numbers:

Factorization Method and Division Method.

Finding the H.C.F. of more than two numbers:

Suppose we have to find the H.C.F. of three numbers, then, H.C.F. of [(H.C.F. of any two) and (the third number)] gives the H.C.F. of three given number.

Similarly, the H.C.F. of more than three numbers may be obtained.

3. Least Common Multiple (L.C.M):

The least number which is exactly divisible by each one of the given numbers is called their L.C.M.

There are two methods of finding the L.C.M. of a given set of numbers:

Factorization Method, Division Method.

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

5. Co-primes:

Two numbers are said to be co-primes if their H.C.F. is 1.

6. H.C.F. and L.C.M. of Fractions:

1. H.C.F. = H.C.F. of Numerators / L.C.M. of Denominators

2. L.C.M. = L.C.M. of Numerators / H.C.F. of Denominators

1. If HCF of two numbers is 11 and the product of these numbers is 363, what is the greater number?

Answer: 33

Explanation:

Let the numbers are 11a and 11b

(11a × 11b ) = 363

121ab = 363

ab = 363 / 121

ab = 3

Co primes with product 3 = ( 1, 3 )

Hence the numbers with HCF 11 and product 363

= ( 11 × 1, 11 × 3 )

= ( 11, 33 )

Hence numbers are 11 and 33 The greater number = 33

7. Find the H.C.F. of 26 × 35 × 52, 28 × 32 × 54 × 72and 27 × 33 × 53 × 74?

Answer: 14400

Explanation:

The H.C.F. of the given numbers is the product of the common factors with least power. H. C. F = 26 × 32 × 52

= ( 2 × 2 × 2 × 2 × 2 × 2 ) × ( 3 × 3 ) × ( 5 × 5 )

= 64 × 9 × 25

= 14400

H.C.F = 14400

8. Find the HCF of 54, 288, 360 ?

Answer: 18

Explanation:

Lets solve this question by factorization method. 18 = 2 × 32

288 = 25 × 32

360 = 23 × 32 × 5

HCF will be minimum term present in all three = 2 × 32 = 18

H.C.F = 18

9. The sum of two numbers is 528 and their H.C.F is 33. Find the number of pairs of numbers satisfying the above condition?

Answer: 4

Explanation:

Let the required numbers be 33a and 33b. Then 33a + 33b = 528

a + b = 16

Now, co-primes with sum 16 are ( 1, 15 ), ( 3, 13 ), ( 5, 11 ) and ( 7, 9 ) Required numbers are ( 33×1, 33×15 ), ( 33×3, 33×13 ), ( 33×5, 33×11 ), ( 33×7, 33×9 )

The number of such pairs is 4.

10. If the L.C.M of two numbers is 750 and their product is 18750, find the H.C.F of the numbers?

Answer: 25

Explanation:

H.C.F = ( Product of the numbers ) / ( Their L.C.M )

= 18750 / 750

= 25

H.C.F = 25

Conclusion

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Problems for practice:

1. Find the HCF and LCM of 70 and 90

2. Product of two co-prime numbers is 117. Then their L.C.M is :

3. Find the greatest number that will divide 149, 247 and 624 leaving remainders 5, 7, 12 respectively.

4. Find the two numbers where LCM is 45 times their HCF. If one of the numbers is 125 and the sum of HCF and LCM is 2300, then the other number is?

5. Find the greatest number which will divide 772 and 2778 so as to leave the remainder 5 in each case.


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