Least Common Multiple (LCM) of 72 and 87
The least common multiple (LCM) of 72 and 87 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 87?
First, calculate the GCD of 72 and 87 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 87 = 0 remainder 72 |
| 2 | 87 ÷ 72 = 1 remainder 15 |
| 3 | 72 ÷ 15 = 4 remainder 12 |
| 4 | 15 ÷ 12 = 1 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 23 | 2277 |
| 48 and 101 | 4848 |
| 85 and 172 | 14620 |
| 83 and 169 | 14027 |
| 138 and 167 | 23046 |