to find LCM and HCF of given numbers by playway method class 6 tell me the answer.
Answers
Answer:
The Lowest Common Multiple (LCM) of two or more given numbers is the lowest (or smallest or least) of their common multiples.
If two numbers are co-prime then the LCM is the product of the two numbers.
Find the LCM of 7 and 13.
7 = 7 x 1 and 13 = 1 x 13
So, LCM is 7 x 13 = 91.
Common multiple method
Find the lowest common multiple of the numbers 8, 12 and 18.
Solution:
List the multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88
List the multiples of 12: 12, 24, 36, 48, 60, 72, 84,
List the multiples of 18: 18, 36, 54, 72, 90, 1
The common multiples of 8, 12 and 18 are 72 ...
L.C.M. of 8, 12 and 18 is 72.
This method works only when there are very small numbers.
Prime factorization method
Find the LCM of 90, 100 and 150.
Solution:
Prime factorisation of the given numbers
90 = 2 x 3 x 3 x 5 = 2 x 32 x 5
100 = 2 x 2 x 5 x 5 = 22 x 52
150 = 2 x 3 x 5 x 5 = 2 x 3 x 52
Let’s find the product of all the factors with highest powers.
22 x 32 x 52 = 4 x 9 x 25 = 900
Common division method of prime factorisation
A very convenient method to find the LCM is the common division method. In this method of prime
factorisation we proceed as follows:
Arrange all the given numbers in a row and separated by commas.
Start with the lowest prime number which divides at least one of the given numbers exactly.
Write down the quotients and any undivided numbers in the next line.
Repeat the process as shown below until 1 is the only common factor.
Find the product of all the divisors. This is the required LCM.
Find the L.C.M. of the numbers 36, 48 and 72.
Solution:
LCM = 2 x 2 x 2 x 2 x 3 x 3 = 144
Word problem
Find the least number which when divided by 18, 28, 32 and 42 leaves a remainder 5 in each case.
Solution:
First we should find the LCM of 18, 28, 32 and 42.
LCM = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 7 = 2016
2016 is the least number which when divided by the given numbers will leave remainder 0 in each case. But we need the least number that leaves remainder 5 in each case.
Therefore, the required number is 5 more than 2016. The required least number = 2016 + 5 = 2021
Question: The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they change simultaneously at 7 a.m., at what time will they change simultaneously again?
Solution:
The time period after which these lights will change = LCM of 48, 72 and 108
LCM = 2 x 2 x 2 x 2 x 3 x 3 x 3 = 432
Therefore, the light will change together after every 432 seconds. i.e 7 min 12 seconds.