In order to understand this concept, we need to learn some words
Factor - One number is said to be a factor of another when it divides the other exactly. Eg- 6 & 7 are factors of 42.
Highest Common Factor - Hcf of two or more numbers is the greatest number that divides each of them exactly. Thus ,6 is the HCF of 18 & 24.Because there is no number greater than 6 that divides both 18 & 24.
eg- HCF of 1365,1560& 1755
1365 = 3*5*7*13
1560 = 2*2*2*3*5*13
1755 = 3*3*3*5*13
HCF = 3*5*13 = 195
Relation between HCF & LCM
HCF(n1,n2) x LCM(n1,n2) = n1 x n2
after expressing the given fractions in lowest terms.
LCM - lcm of two or more given numbers is the least number which is exactly divisible by each of them.
15 is a common multiple of 3 & 5
LCM of 8, 12, 15, 21
8= 2*2*2*
12= 2*2*3
15 = 3*5
21= 3*7
Here, the prime factors that occur in the given numbers are 2, 3, 5, 7 and their highest powers are respectively 2*2*2, 3, 5, & 7.
Hence , the required LCM = 2*2*2**3*5*7= 840
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Ex1: The LCM of two numbers is 2079 and their HCf is 27. If one of the numbers is 189, find the other ?
sol. the required number= LCM * HCF /first number= 2079*27/189 = 297
Some questions on this topic
Q1. Find the least number of square tiles required to pave the ceiling of a hall 15m 17cm long and 9m 2cm broad.
Ans - 814
Q2. Find the HCF & LCM of 4/5, 5/6, 7/15?
Ans - HCF = 1/30
LCM = 140
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HCF of decimals
step 1 -first of all , we make the same no. of decimal places by putting zero or zeroes in the given no .It is done only when the nos have different decimal places i.e. 1.3,1.32
step II - find the HCF of the given numbers without taking decimals into consideration i.e. as integers
step III - put in the result , i.e. HCF as many decimal places as there are in each of the numbers after making them same in step 1.
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