Least Common Multiple (LCM) of 72 and 116
The least common multiple (LCM) of 72 and 116 is 2088.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 72 and 116?
First, calculate the GCD of 72 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 116 = 0 remainder 72 |
| 2 | 116 ÷ 72 = 1 remainder 44 |
| 3 | 72 ÷ 44 = 1 remainder 28 |
| 4 | 44 ÷ 28 = 1 remainder 16 |
| 5 | 28 ÷ 16 = 1 remainder 12 |
| 6 | 16 ÷ 12 = 1 remainder 4 |
| 7 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 138 | 8970 |
| 85 and 113 | 9605 |
| 138 and 126 | 2898 |
| 157 and 178 | 27946 |
| 148 and 93 | 13764 |