Q5 Find HCF and LCM of 17,13 29 by prime factorization method
Answers
Answer:
The Highest Common Factor (HCF) is the largest common divisor or gcd of two or more positive integers, as the mathematics rules dictate, appears to be the largest positive integer that divides the numbers without leaving a remainder.
Example:
Consider the two number 8 and 12.
As the highest number that can divide both 8 and 12 is 4.
Therefore, the H.C.F. of 8 and 12 would be 4.
In arithmetic, Least common multiple LCM (a,b) is the least common multiple of two numbers, a and b. And the LCM is the smallest or least positive integer that is divisible by both a and b.
Example:
Consider the two number 8 and 12 and let us write the multiples of two numbers.
Multiples of 8 = 16, 24, 32, 40 ,48, 56……
Multiples of 12 = 24, 36, 48, 60, 72………
From the above list, we can observe that least common multiples of 8 and 12 is 24.
I.e LCM (8, 12) = 24
Let us find the HCF of 17,23,29
17 = 17 × 1
23 = 23 × 1
29 = 29 × 1
∴ HCF (17,23,29) = 1
Let us find the LCM of17,23,29
LCM(17,23,29) = 17 × 23 × 29
∴ LCM(17,23,29) = 11339
Let us verify LCM and HCF is equals to the product of three numbers
LCM × HCF =17 × 23 × 29
17 × 23 × 29 × 1 =17 × 23 × 29
11339 = 11339