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August 26, 2023
On this page we have discussed LCM and HCF formulas, definition with examples.
LCM stands for Least Common Factor
LCM or least common factor of two numbers 4, 6 is denoted as LCM(4, 6). And the LCM is the smallest positive integer that is divisible by both 4 and 6, which is 12.
HCF stands for Highest Common Factor
Greated Common Divisor or gcd of two or more positive integers is defined as the largest positive integer that divides the numbers without leaving the remainder.
Take an example of finding the highest common factor of 100, 125 and 180.Now let us write the prime factors of 100, 125 and 180.100 = 2 × 2 × 5 × 5125 = 5 × 5 × 5180 = 3 × 3 × 2 × 2 × 5The common factors of 100, 125 and 180 are 5Therefore, HCF (100, 125, 180) = 5
Steps to find the HCF of any given numbers:
Example:
Let’s take two number 120 and 180
120) 180 (1 120 --------- 60) 120 (2 120 --------- 000
A technique to find the Least Common Multiple (LCM) of a set of numbers by breaking down each number into its prime factors and then multiplying the highest powers of each prime factor.
Lets take two numbers i.e., 25 and 35, now to calculate the LCM:
If the same multiple occurs more than once in both the given numbers, then multiply the factor by the most number of times it occurs.The occurrence of Numbers in the above example:5: two times7: one timeLCM = 7 × 5 × 5 = 175
Let us see with the same example, which we used to find the LCM using prime factorization.Solve LCM of (25,35) by division method.
5 | 25, 35----------5 | 5, 7---------7 | 1, 7--------- | 1, 1
Therefore, LCM of 25 and 35 = 5 x 5 × 7 = 175
Question:
Calculate the highest number that will divide 43, 91 and 183 and leaves the same remainder in each case
Options
A. 4B. 7C. 9D. 13
Solution:
Here the trick is :
We have here 43, 91 and 183
So differences are
183 – 91 = 92,183 – 43 = 140,91 – 43 = 48.
Now, HCF (48, 92 and 140)
And 4 is the required number.
Correct Answer : A
Which of the following is greatest number of four digits which is divisible by 15, 25, 40 and 75 is:
A. 9700B. 9600C. 9800D. 9650
Solution: Greatest number of 4-digits is 9999.
Now , find the L.C.M. of 15, 25, 40 and 75 i.e. 600.
On dividing 9999 by 600, the remainder is 399.
Hence, Required number (9999 – 399) = 9600.
Alternatively,
\frac{9999}{600} = 16.66500
Ignore the decimal points, required number would be 16 * 600 = 9600
Correct Answer : B
The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:
A. 25 cmB. 15 cmC. 35 cmD. 55 cm
Solution: Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm.
Correct Answer : C
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Nice explanation 😊 Got placed in Intel and cisco thanks to you guys
Thats very cool !!! All the very best for your future
Awesome explanation!
This is the best page to prepare for online test…..