General Awareness:--Aptitude Part 1
H.C.F and L.C.M of numbers and patterns
Why is L.C.M. and H.C.F. important?
The chapter of Highest Common factor and L.C.M is very important. This concept is useful in the chapters of time and distance, time and work,
pipes and cisterns, etc. The tricks and method used to find Least Common multiple and Highest Common factor of two or more numbers help in finding out quick solutions and thus reduce time during exams.
Least Common multiple concept is important to solve problems related to racetracks, traffic lights, etc.
Highest Common factor concept is useful in calculating the largest size of tile/room in particular area, largest tape to measure the land, etc.
The chapter of Highest Common factor and L.C.M is very important. This concept is useful in the chapters of time and distance, time and work,
pipes and cisterns, etc. The tricks and method used to find Least Common multiple and Highest Common factor of two or more numbers help in finding out quick solutions and thus reduce time during exams.
Least Common multiple concept is important to solve problems related to racetracks, traffic lights, etc.
Highest Common factor concept is useful in calculating the largest size of tile/room in particular area, largest tape to measure the land, etc.
Important terms:
1) Factors meaning: Factor is a number in which exactly divides other number.
Example: 2 and 3 are factors of 6
2) Multiple meaning: A number is said to be multiple of another number, when it is exactly divisible by other number.
Example: 6 is a multiple of 3 and 2
3) Common multiple meaning: A common multiple of two or more numbers is such a number which is exactly divisible by each of them.
Example: 12 is a common multiple of 2,3,6
4) Highest Common factor/G.C.F: (Highest Common Factor / Greatest Common Factor). H.C.F of two or more numbers is the such greatest number which divides each number exactly.
5) L.C.M. meaning: (Lowest common multiple). The least number exactly divisible by each one of the given such numbers is called least common multiple.
Example: 2 and 3 are factors of 6
2) Multiple meaning: A number is said to be multiple of another number, when it is exactly divisible by other number.
Example: 6 is a multiple of 3 and 2
3) Common multiple meaning: A common multiple of two or more numbers is such a number which is exactly divisible by each of them.
Example: 12 is a common multiple of 2,3,6
4) Highest Common factor/G.C.F: (Highest Common Factor / Greatest Common Factor). H.C.F of two or more numbers is the such greatest number which divides each number exactly.
5) L.C.M. meaning: (Lowest common multiple). The least number exactly divisible by each one of the given such numbers is called least common multiple.
What is Prime number?
- Consider this number : 12. This number can be found in many multiplication tables for example
- 1 x 12=12.
- 2 x 6 =12
- 3 x 4=12
- That means, 12 has many factors (1,2,3,4,6,12). Such number is called a composite number.
- On the other hand, consider this number: 29. We cannot find it in any table but except 29 x 1 =29. Such number is called a prime number.
- Let’s make a shortlist from exam point of view
| Prime | Non-prime (composite) |
| 2,3,5,7,11,13,17,19,23,29 | 4,6,8,9,10,12,14,15…. |
Highest Common factor & LCM of fractions:
Formula for finding the HCF & LCM of a fractional number is given below.
Highest Common factor of fraction = HCF of numerator / LCM of denominator
Least Common factor of Fraction = LCM of Numerator / HCF of Denominator
Examples:
Find the greatest number that will divide these numbers 43, 91 and 183 so as to leave the same remainder in each case.
Required number = Highest Common factor of numbera (91 - 43), (183 - 91) and (183 - 43)
= H.C.F. of 48, 92 and 140
= 4.
The Highest Common factor of two numbers is 23 and the other two factors of their Least Common multiple are 13 and 14. The larger of the two numbers is:
It is clearly seen the numbers are (23 x 13) and (23 x 14).
Larger number = (23 x 14) = 322.
Let N will be the greatest number that will divide these numbers 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:
N = Highest Common factor of (4665 - 1305), (6905 - 4665) and (6905 - 1305)
= Highest Common factor of 3360, 2240 and 5600 = 1120.Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4
The greatest number of four digits in which is completely divisible by 15, 25, 40 and 75 is:
Greatest number of 4-digits is 9999.
Least Common multiple of 15, 25, 40 and 75 is 600.
On dividing 9999 by number 600, the remainder is 399.
Required number (9999 - 399) = 9600.
The product of two numbers is 4107. If the Highest Common factor of these numbers is 37, then the greater number is: Let the numbers be 37a and 37b.
Then, 37a x 37b = 4107
ab = 3.
Now, co-primes with product 3 are (1, 3).
So, the required numbers are in sequence (37 x 1, 37 x 3) i.e., (37, 111).
Greater number = 111.
Do it Yourself:------
The G.C.D. of 1.08, 0.36 and 0.9 is:| A. | 0.03 |
| B. | 0.9 |
| C. | 0.18 |
| D. | 0.108 |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| A. | 74 |
| B. | 94 |
| C. | 184 |
| D. | 364 |
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