Arithmetic aptitude :: HCF and LCM :: General Questions

• HCF and LCM - General Questions
• HCF and LCM - Important Formulas and Facts

Factors and Multiples:
If number x divided another number y exactly, we say that x is a factor of y.
and y is called a multiple of x.
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 them exactly.
Mehods To Find HCF
Factorization Method:
Step 1) Find the prime factors of each number
Step 2) Find the product of all common prime factors, which is the HCF of given numbers
e.g. To find the HCF of 14 and 8
14 = 2 x 7
8 = 2 x 2 x 2
HCF = 2
Division Method:
To find the H.C.F. of two given numbers
Step 1)Divide the larger by smaller one.
Step 2)Divide the divisor by the remainder.
Step 3)Repeat the process of dividing the preceding number by the remainder last obtained till zero is obtained as remainder.
The last divisor is the required H.C.F.
Finding the H.C.F. of more than two numbers:
Step 1)H.C.F. of [(H.C.F. of any two) and (the third number)] gives the H.C.F. of three given number.
Similarly, we can find the H.C.F. of more than three numbers.
Least Common Multiple (L.C.M.):
LCM is the least number which is exactly divisible by each one of the given numbers.
Methods to find LCM
Factorization Method:
Step 1)Find prime number factors of each given number.
Step 2)Find the product of highest powers of all the prime number factors, which gives the LCM of given numbers
e.g. To find the LCM of 14 and 8
14 = 2 x 7
8 = 2 X 2 x 2 = 2 ³
LCM = 2 ³ x 7 = 56
Division Method (short-cut):
Step 1)Arrange the given numbers in a rwo in any order.
Step 2)Divide by a number which divided exactly at least two of the given numbers and carry forward the numbers which are not divisible.
Step 3)Repeat the above process till no two of the numbers are divisible by the same number except 1.
LCM = The product of the divisors and the undivided numbers
Product of two numbers = (HCF x L.C.M) of two numbers.
Co-primes: Co-primes means, if their H.C.F. is 1.
HCF and LCM of Fractions:
HCF = (HCF of Numerators) / (LCM of Denominators)
LCM = (LCM of Numerators) / (HCF of Denominators)
H.C.F. and L.C.M. of Decimal Fractions:
In a given numbers,
Step 1)Make the same number of decimal places by annexing zeros in some numbers, if necessary.
Step 2)Considering these numbers without decimal point, find H.C.F. or L.C.M.
Step 3)In the result, mark off as many decimal places as are there in each of the given numbers.
Comparison of Fractions:
Step 1)Find the L.C.M. of the denominators of the given fractions.
Step 2)Convert each of the fractions into an equivalent fraction with L.C.M as the denominator, by multiplying both the numerator and denominator by the same number. The resultant fraction with the greatest numerator is the greatest.

The LCM of two numbers is 45 times their HCF. If one of the numbers is 125 and the sum of HCF and LCM is 1150, the other number is :

Answer:

Explanation:

LCM = 45 x HCF
LCM + HCF = 1150
45 x HCF + HCF = 1150
46 x HCF = 1150
HCF = 25
Then,
LCM = 45 x 25 = 1125.
Now, use the formula,
1st number x second Number = LCM x HCF
125 x second number = 1125 x 25
Second Number = 225.

The product of the L.C.M. and H.C.F of two numbers is 24. The difference of two numbers is 2. Find the numhers

Answer:

Explanation:

Let the number are a and b

From the question we get,

a - b = 2
b = a-2
a (a-2) = 24
a2- 2a - 24 = 0
(a+4)(a-6) = 0
a = - 4 or a = 6

So the numbers are 4 and 6

The H.C.F. of two numbers is 11 and their L.C.M. is 7700. If one or the numbers is 275, then the other is :

Answer:

Explanation:

Product of HCF and LCF
11 * 7700 = 84700
Other number = (84700 / 275) = 308

Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two a 1073. The sum of the three numbers is :

Answer:

Explanation:

In HCF, will get a number which is common to both numbers 551 and 1073.

So hcf of 551 and 1073 is 29, which is one number among three numbers.

Let other two numbers be x and y

Given, x*29=551

x=551/29 = 19


Now,
y*29=1073
y = 2073/29 = 37

The three numbers. are 29,19,37

Sum = 29+19+37 = 85

The sum of two numbers is 528 and their H .C.F. is 33. The number of pairs of numbers satisfying the above conditions is :

Answer:

Explanation:

Let the required numbers be 33x and 33y.

Then 33x +33y= 528   

=> x+y = 16.

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

Therefore, required numbers are ( 33 x 1, 33 x 15), (33 x 3, 33 x 13), (33 x 5, 33 x 11), (33 x 7, 33 x 9)

The number of such pairs is 4.

• HCF and LCM - General Questions