H.C.F and L.C.M word problems (Part-1)
H.C.F and L.C.M word problems.
Introduction
In this article we have given about how to solve HCM and LCM problems. HCF and LCM formulas are given for clear understanding by the users on Nithra Jobs site. It will be easy method for understanding and learning.
Formulas to use :
1. Factors and Multiples:
If number a divided 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
Solved Problems:
1. Find the H.C.F of 24 × 32 × 53 × 72 × 9, 22 × 32 × 54 × 72, 72 × 93 × 22
Answer: 196
Explanation:
The Prime numbers common to given numbers are 7, 2
H.C.F = 72 × 22
= ( 7 × 7 ) × ( 2 × 2 )
= 49 × 4
= 196
The H.C.F = 196
2. Find the H.C.F of 108, 288 and 72.
Answer: 36
Explanation:
108 = 22 × 33
288 = 25 × 32
72 = 23 × 32
H.C.F = 22 × 32
= ( 2 × 2 ) × ( 3 × 3 )
= 4 × 9
= 36
The H.C.F = 36
3. Find the L.C.M of 360, 2100, 216
Answer: 37800
Explanation:
360 = 23 × 32 × 5
2100 = 22 × 52 × 3 × 7
216 = 23 × 33
L.C.M = 23 × 33 × 52 × 7
= ( 2 × 2 × 2 ) × ( 3 × 3 × 3 ) × ( 5 × 5 ) × 7
= 8 × 27 × 25 × 7
= 216 × 25 × 7
= 216 × 175
= 37800
The L.C.M = 37800
4. The ratio of two numbers is 3 : 5 and their H.C.F is 4. Their L.C.M is :
Answer: 12, 20
Explanation:
Let the numbers be 3x and 4x Then their H.C.F = x
So x = 4 So the number = 3x
= 3 × 4
= 12
Another number = 5x
= 4 × 5
= 20
The numbers are 12, 20.
5. Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
Answer: 4
Explanation:
Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)
= H.C.F. of 48, 92 and 140
= 4.
The greatest number is 4.
Conclusion
Keep on learning the above given HCF and LCM questions and answers regularly in Nithra jobs site. By gaining the knowledge in this topic we can easily attend and solve the HCF and LCM problems for tnpsc.
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