take 3 and 5 . find their lcm and hcf and write your observations
Answers
Step-by-step explanation:
What is your observation? Take two multiples of any number. What is their LCM?
Let the number be x and let the two multiples of x be ax and bx.
So, we come down to finding the LCM of ax and bx.
Since x is common to both, we need to consider it just once and that leaves a and b. At this point, there are 2 possibilities:
a and b are relatively prime i. e. GCD(a, b) = 1. In this case, the LCM of ax and bx is simply x*a*b.
a and b are not relatively prime i. e. they share a common multiple, say k, which in other words is GCD(a, b) = k. In this case, the LCM of ax and bx is x*a*b / k.
Very generically, the answer for LCM of ax and bx could be given as:
(x*a*b) / GCD(a,b). If GCD is 1 then it’s case 1 else it’s case 2.
Answer:
3 and 5
their l.cm. will be
3 = 1 × 3
5 = 1 × 5
= 3 × 5 × 1
= 15
and hcf is = 1
bcoz 1 is common multiple of 3 and 5