How to find two numbers whose HCF is 179 and their LCM is 2685?

The HCF of two numbers is 179 and their LCM is 2685. What are the numbers? The two numbers are (179, 2685) or (537, 895). How to calculate it? Three methods, one automatic method and two manual methods.

First of all, What are the HCF and LCM?

HCF is short for highest common factor, which refers to the biggest number that divides more than 2 numbers without leaving a remainder. It is called by many names – greatest common factor (GCF), greatest common divisor (GCD) and highest common divisor (HCD).

LCM stands for least common multiple, which refers to the smallest positive integer that is divisible by 2 numbers. It is called by many names – Lowest Common Multiple (LCM), Smallest Common Divisor (SCD), Lowest Common Denominator (LCD) and Least Common Factor (LCF).

Now, let’s go to the concrete solutions.

Calculate with the calculator: Find Two Numbers by HCF and LCM.

Enter the HCF 179 in the first input box, enter the LCM 2685 in the second input box. Then click Calculate button and the answer will be displayed immediately. The two numbers are (179, 2685) or (537, 895).

This method is fast, convenient, and error-free. Suitable for everyone, especially the layman.

According to the question, the HCF of two numbers is 179. So, we can assume that the two numbers are 179x and 179y. x and y are positive integers and coprime.

Based on the formula, the product of two numbers is equal to the product of their HCF and LCM. So, we can get the equation

179x * 179y = HCF(179x, 179y) * LCM(179x, 179y)
32041xy = 179 * 2685
xy = 15

There are 2 pairs of two positive integers whose product is 15.

(1, 15), (3, 5)

All of them are co-prime numbers.

Now, 2 pairs of coprime multiplied by the greatest common divisor 179 are the numbers we want.

(1 * 179, 15 * 179) = (179, 2685)
or
(3 * 179, 5 * 179) = (537, 895)

So, the two numbers are

(179, 2685) or (537, 895)

Since the LCM of two numbers is 2685, the two numbers must be factors of 2685. So, we can calculate the factors of 2685 first. Then, find the two numbers in the factors whose HCF is 179.

With the find all factors calculator, we can easily get the factors of 2685 are

1, 3, 5, 15, 179, 537, 895, 2685

Among them, numbers divisible by 179 are

179, 537, 895, 2685

This means that their greatest common divisor maybe 179.

According to the formula, the product of two numbers is equal to the product of their HCF and LCM. So, we can get the product of these two numbers is

HCF * LCM = 179 * 2685 = 480615

Among the numbers that are divisible by 179, we can find that there are 2 pairs of numbers whose product is 480615.

179 * 2685 = 480615
537 * 895 = 480615

So, the two numbers are (179, 2685) or (537, 895).

There are 2 pairs of numbers whose HCF is 179 and their LCM is 2685.

(179, 2685) or (537, 895)

And their product is 480615.