What is the LCM of 14 and 36?

To find the LCM (Least Common Multiple) of 14 and 36, we can use different methods such as prime factorization, listing multiples, or using the formula.

Here’s one way to find the LCM of 14 and 36 using prime factorization:

Step 1: Find the prime factorization of each number: 14 = 2 x 7 36 = 2 x 2 x 3 x 3

Step 2: Write down the prime factors of both numbers, including duplicates: 2 x 2 x 3 x 3 x 7

Step 3: Multiply all the prime factors together: 2 x 2 x 3 x 3 x 7 = 252

Therefore, the LCM of 14 and 36 is 252.

Another way to find the LCM is to list multiples of each number until you find the smallest multiple that they have in common. This method is more time-consuming and may not be practical for larger numbers.

Alternatively, we can use the formula for LCM, which is:

LCM(a, b) = |a x b| / GCD(a, b)

where a and b are the numbers, GCD(a, b) is the greatest common divisor of a and b, and “|” denotes absolute value.

Using this formula, we can find the LCM of 14 and 36 as follows:

GCD(14, 36) = 2 (which can be found using the Euclidean algorithm or by inspection of the prime factorization)

LCM(14, 36) = |14 x 36| / GCD(14, 36) = (14 x 36) / 2 = 252

Again, we get the same answer, which is 252.