Relation between lcm and gcd of 3 numbers
Answers
for 2 lcm=product of 2 no./hcf
Answer:
There's an answer!
Step-by-step explanation:
I don't know if I was the first one to discover that (probably not), but here it is:
LCM (p,q,r) = [ HCF (p,q,r) × LCM (p,q) × LCM (p,r) × LCM (q,r) ] ÷ p × q × r
This is the formula that I've discovered right now abou the relationship between the HCF and LCM of 3 numbers.
But there's a much simpler way to find the LCM and HCF of 3 numbers, but it doesn't include any relationship formula.
To find HCF, do factorization with prime numbers. It's very simple.
To find LCM you do the following:
1) Factorize each one of the numbers separately.
2) Find the largest number of times a same prime number appears with each one of the prime numbers in each one of the separated factorization.
3) Multiply all the prime numbers by the number of times they appear, then multiply all of the products together.
Example: LCM (12,42,90)
Prime factors of 12 -> 2, 2, 3
Prime factors of 42 -> 2, 3, 7
Prime factors of 90 -> 2, 3, 3, 5
Largest number of times that each prime number appears:
2 -> 2 times (in the factorization of 12)
3 -> 2 times (in the factorization of 90)
5 -> 1 time
7 -> 1 time
2 × 2 = 4
3 × 2 = 9
5 × 1 = 5
7 × 1 = 7
4 × 9 × 5 × 7 = 1260
LCM (12,42,90) = 1260
Obtaining the LCM with the formula:
LCM (12,42,90) = [ GCD (12,42,90) × LCM (12,42) × LCM (12,90) × LCM (42,90) ] ÷ 12 × 42 × 90
LCM (12,42,90) = [ 6 × 84 × 180 × 630 ] ÷ 45360
LCM (12,42,90) = 1260