The product of two numbers is 840. Find their LCM.

To find the LCM (Least Common Multiple) of two numbers, we need to determine the smallest multiple that is divisible by both numbers. In this case, we are given that the product of the two numbers is 840. Let's break down the process of finding the LCM step by step:

Step 1: Prime Factorization
The first step is to find the prime factorization of the given number, 840. Prime factorization involves breaking down a number into its prime factors.

840 can be factored as follows:

840 = 2 * 2 * 2 * 3 * 5 * 7

Step 2: Identifying Common Prime Factors
Now, we need to identify the common prime factors between the two given numbers. Since we only have one number (840) in this case, we can consider its prime factors as the common prime factors.

The common prime factors of 840 are:
2, 2, 2, 3, 5, 7

Step 3: Constructing the LCM
To find the LCM, we need to take the highest power of each common prime factor. In other words, we select the prime factors with the highest exponent.

From the common prime factors, we have:
2^3 * 3^1 * 5^1 * 7^1

Step 4: Calculating the LCM
Finally, we calculate the LCM by multiplying the selected prime factors together.

LCM = 2^3 * 3^1 * 5^1 * 7^1
= 8 * 3 * 5 * 7
= 840

Therefore, the LCM of the numbers is 840.

Summary:
To find the LCM of two numbers, we first determine the prime factorization of the given numbers. Then, we identify the common prime factors and select the highest power of each factor. Finally, we calculate the LCM by multiplying the selected prime factors together. In this case, the LCM of the numbers is 840.

420 is the answer but how?