What is the ratio between the lcm and hcf of 5,15, and 20 ?
To find the HCF and LCM of three given numbers that is 5, 15, and 20. We must find the prime factors of all the above given number. But before we calculate the LCM and HCF of above given number. Let's understand the term HCF and LCM. And also establish a relationship between HCF and LCM.
What is HCF and LCM ?
HCF stands for highest common factor. Suppose we have two natural numbers that is A and B respectively. Now, if the prime factor of a given number A will be a, b, c and d. And the prime factors of B is x, y, and z.
Prime factors of
A = a, b, c, and d.
B = x, y, and z.
And a>b>c>d or x>y>z.
Then HCF of A and B will be a or x respectively.
In simple words, if we have two natural numbers given. Then the relation between HCF and LCM of two number is the product of two number is equal to the product of HCF and LCM.
But here we have three numbers 5, 15, and 20.
Hence, the relation between HCF and LCM of three numbers is the LCM of three number will be equal to the multiple of three numbers with the HCF of three numbers and divide it by the HCF of two number adjecently.
What is the ratio between the lcm and hcf of 5,15, and 20 ?
Here are the solution of the ratio between the lcm and hcf of 5,15, and 20.
HCF of 5, 15 and 20.
5 = 1 × 5
15 = 1 × 5 × 3
20 = 1 × 2 × 2 × 5
Now, in all the three cases of prime factors. The highest number is 5. Hence, the HCF of 5, 15 and 20 is 5.
LCM of 5, 15 and 20.
5|(5, 15, 20)
1|(1, 3, 4)
(1, 3, 4)
Hence, the LCM of 5, 15 and 20 is 5 × 1× 3 × 4 is 60.
Here, we have got the HCF that is 5 and LCM that is 60.
Now, the ratio between the LCM and HCF of 5, 15 and 20 is
60 : 5 = 12 : 1