Free 11 Plus LCM and HCF Practice Papers
Free 11 Plus LCM and HCF Practice Papers
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Free 11 Plus LCM and HCF Practice Papers
LCM and HCF are among the most commonly used topic in mathematics. They form the fundamentals for solving different quantitative problems.
Questions on LCM and HCF appear in the 11 plus entrance exams conducted by different 11 plus grammar schools, independent schools and other private schools.
For example, LCM and HCF are important for solving time and speed, time and work-related problems.
For a clear understanding of these concepts, we need to look into the buzz words Factors and Multiples.
Factor:
The number that divides the given positive integer without leaving any remainder is called the factor.
For example, 24 ÷ 8 gives remainder=0.
Hence 8 is the factor of 24.
Multiple:
Multiple of a number is the result of multiplying a number by a whole number.
For example, the multiples of 4 can be obtained as
(4×1)=4, (4×2)=8,(4×3)=12,….. and so on.
Let us look at the definition of each acronym:
LCM:
It is an acronym for “ Least Common Multiple”. It is the least number which is exactly divisible by each of the given numbers.
HCF:
It is an acronym for “ Highest Common Factor “. It is the largest number that divides each of the given numbers. HCF is also called by the name GCD ( Greatest Common Divisor).
The next question is how to compute them.
Finding LCM:
Given to find the LCM of 6 and 8, we proceed as follows:
List out the multiples of 6 and 8
The multiples of 6 are: 6×1=6, 6×2=12, 6×3=18, 6×4=24, 6×5=30,
The multiples of 8 are: 8×1=8, 8×2=16, 8×3=24, 8×4=32, 8×5=40,
The lowest and common multiple of both 6 and 8 is 24.
Hence LCM of 6 and 8 is 24.
Finding HCF:
To compute the HCF of 6 and 12, we proceed as follows:
List out the factors of 6 and 12
The factors of 6 are: 1,2,3 and 6
The factors of 12 are: 1,2,3,4,6 and 12
The highest and common factor of both 6 and 12 is 6.
Hence LCM of 6 and 12 is 6.
Compute HCF and LCM using prime factors:
We employ this method when given numbers are large such that listing out all the factors and multiples for each number would be a difficult task.
Example problems on 11 Plus LCM and HCF:
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