Least Common Multiple (LCM) of 72 and 99
The least common multiple (LCM) of 72 and 99 is 792.
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 99?
First, calculate the GCD of 72 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 99 = 0 remainder 72 |
| 2 | 99 ÷ 72 = 1 remainder 27 |
| 3 | 72 ÷ 27 = 2 remainder 18 |
| 4 | 27 ÷ 18 = 1 remainder 9 |
| 5 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 176 | 4752 |
| 178 and 56 | 4984 |
| 76 and 43 | 3268 |
| 41 and 157 | 6437 |
| 74 and 178 | 6586 |