Find the LCM and HCF of 510 and 92. Verify LCM and HCF is equal to the product of two numbers.
The Least Common Multiple (LCM) of two or more numbers is the smallest number among all common multiples of the given numbers. The Highest Common Factor (HCF) of two numbers is the highest possible number which divides both the numbers completely. Let us find the LCM and HCF of 510 and 92 and verify if the LCM and HCF is equal to the product of these two numbers.
Answer: The LCM of 510 and 92 is 23460 and the HCF is 2. The product of the two numbers is equal to the product of their LCM and HCF, 510 × 92 = 23460 × 2
Let us find the HCF and LCM of 510 and 92 and verify that its product is equal to 510 × 92.
Explanation:
Let us find the LCM (Least common multiple) and HCF (Highest common factor) of 510 and 92 by the division method.
LCM of 510 and 92 by Common Division Method
In this division method, we divide the numbers simultaneously with prime numbers and stop when we don't have a prime number to divide the given numbers. The product of all the prime numbers used for division is the LCM of 510 and 92.
So, the LCM of 510 and 92 is 23460.
HCF of 510 and 92 by Long Division
-
Step 1: Divide 510 by 92 and check the remainder.
-
Step 2: Make the remainder of the above step as the divisor and the divisor of the above step as the dividend and perform the long division again.
-
Step 3: Continue till you get the remainder as 0
So, the HCF of 510 and 92 is 2.
Let us verify the products: LCM (510, 92) × GCF (510, 92) = Product of the numbers 510 and 92
LCM (510, 92) × GCF (510, 92) = 23460 × 2 = 46920
Product of the numbers 510 × 92 = 46920