# The ratio between the HCF and LCM of 5, 15 and 20 is?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

**The ratio between the HCF and LCM of 5, 15, and 20 is 1:12. HCF** (Highest Common Factor) is the largest factor that two or more numbers have in common. Whereas, **LCM** (Least Common Multiple) is the smallest multiple that two or more numbers have in common. While the HCF focuses on finding the largest factor that divides the given numbers, the LCM focuses on finding the smallest multiple that is divisible by the given numbers.

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## Difference Between HCF and LCM

The HCF (Highest Common Factor) and LCM (Least Common Multiple) are mathematical terms used to describe relationships between numbers.

**HCF (Highest Common Factor):**

The HCF of two or more numbers is the largest positive integer that divides each of the given numbers without leaving a remainder. It is also known as the greatest common divisor (GCD). The HCF is useful for finding the largest common factor between numbers and simplifying fractions.

**For example**, the HCF of 12 and 18 is 6 since 6 divides both 12 and 18 without leaving a remainder.

**LCM (Least Common Multiple):**

The LCM of two or more numbers is the smallest positive integer that is divisible by each of the given numbers without leaving a remainder. In other words, it is the smallest common multiple of the numbers. The LCM is helpful when dealing with situations that involve multiple cycles or repetitions, such as finding a common denominator for fractions.

**For example**, the LCM of 4 and 6 is 12 since 12 is the smallest number that is divisible by both 4 and 6.

**Solution:**

To find the ratio between the highest common factor (HCF) and least common multiple (LCM) of three numbers (5, 15, and 20), we first need to determine the HCF and LCM of these numbers.

**Step 1:** Finding the HCF (Highest Common Factor)

The prime factorization of the given numbers is as follows:

5 = 5

15 = 3 * 5

20 = 2^{2} * 5

To find the HCF, we take the product of the common prime factors with their minimum powers:

HCF = 5

**Step 2: **Finding the LCM (Least Common Multiple)

To find the LCM, we take the product of the prime factors with their maximum powers:

LCM = 2^{2} * 3 * 5 = 60

The ratio of HCF to LCM is given by:

HCF:LCM = 5:60

Simplifying the ratio, we divide both values by 5:

HCF:LCM = 1:12

Therefore, the ratio between the HCF and LCM of 5, 15, and 20 is 1:12.

**Summary:**

## The ratio between the HCF and LCM of 5, 15 and 20 is?

The ratio between the HCF and LCM of 5, 15, and 20 is 1:12. HCF (Highest Common Factor) and LCM (Least Common Multiple) are mathematical terms used to describe relationships between numbers. While they are related concepts, they serve different purposes and represent different aspects of number relationships.

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