Chapter : Real Numbers
Examples to Find H.C.F. and L.C.M using formulas
Example : Given that H.C.F. (306, 657) = 9, Find the L.C.M. of (306, 657).
Solution: H.C.F. (306, 657) = 9 means H.C.F. of 306 and 657 = 9
Required L.C.M. (306, 657) means required L.C.M. of 306 and 657.
For any two positive integers; their L.C.M. = 
i.e., L.C.M. (306, 657) = 
= 22,338.
Example: Given that L.C.M. (150, 100) = 300, find H.C.F. of (150, 100).
Solution. L.C.M. (150, 100) = 300
↠ L.C.M. of 150 and 100 = 300
Since, the product of number 150 and 100 = 150 × 100
And, we know : H.C.F. (150, 100) = 
= 
= 50.
Example : The H.C.F. and L.C.M. of two numbers are 12 and 240 respectively. If one of these numbers is 48; find the other numbers.
Solution: Since, the product of two numbers = Their H.C.F. × Their L.C.M.
→ One no. × other no. = H.C.F. × L.C.M.
Other no. = 
= 60.
Example: Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 + 5 are composite numbers.
Solution: Since, 7 × 11 × 13 + 13 = 13 × (7 × 11 + 1) = 13 × 78 = 13 × 13 × 3 × 2;
that is, the given number has more than two factors and it is a composite number.
Similarly, 7 × 6 × 5 × 4 × 3 + 5
= 5 × (7 × 6 × 4 × 3 + 1)
= 5 × 505 = 5 × 5 × 101
→ The given no. is a composite number.
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