Q.2.Solve the following. (Any 3)
(1) Find HCF and LCM. 72, 12, 84.
Answers
Answer:
We know that the factors of a number are exact divisors of that particular number. Let’s proceed to the highest common factor (H.C.F.) and the least common multiple (L.C.M.).
HCF (Highest Common Factor)
As the rules of mathematics dictate, the greatest common divisor or the gcd of two or more positive integers happens to be the largest positive integer that divides the numbers without leaving a remainder. For example, take 8 and 12. The H.C.F. of 8 and 12 will be 4 because the highest number that can divide both 8 and 12 is 4.
LCM (Least Common Multiple)
In arithmetic, the least common multiple or LCM of two numbers say a and b, is denoted as LCM (a,b). And the LCM is the smallest or least positive integer that is divisible by both a and b. For example, let us take two positive integers 4 and 6.
Multiples of 4 are: 4,8,12,16,20,24…
Multiples of 6 are: 6,12,18,24….
The common multiples for 4 and 6 are 12,24,36,48…and so on. The least common multiple in that lot would be 12. Let us now try to find out the LCM of 24 and 15.
LCM of 24 and 15
Step-by-step explanation: