Question

Find the HCF and LCM of 2923, 3239

Answer 1

Hint: The Highest common factor of two numbers is the largest number that can divide both the given numbers. The Lowest common multiple of two numbers is the smallest number which can be divided by both of the given numbers. If a, and b are the two numbers, and H and L are their Highest common factor and Lowest common multiple respectively, then we can use the formula \[ab=HL\], which means that the product of two numbers is the same as the product of their highest common factor and lowest common multiple.

Complete step-by-step solution:
We are given two numbers as 2923 and 3239. We need to find their HCF and LCM, first let’s find their HCF. To do this we will express the number in factor form, as follows
\[2923=37\times 79\And 3239=41\times 79\]
As we can see that both numbers have 79 as their largest common factor, thus the HCF of the numbers is 79. We can find the Lowest common multiple or LCM by using the property that the product of two numbers is the same as the product of their highest common factor and lowest common multiple. We get,
\[\Rightarrow 2923\times 3239=79\times LCM\]
Solving the above equation, we get
\[\Rightarrow LCM=119843\]
Hence, the LCM of the two numbers is 119843.

Note: To solve these types of problems, it is easier to find the highest common factor first and then the lowest common multiple using the formula. Finding the HCF of a number is easier than finding the LCM of any two given numbers.