Least Common Multiple (LCM) of 72 and 102
The least common multiple (LCM) of 72 and 102 is 1224.
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 102?
First, calculate the GCD of 72 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 72 ÷ 102 = 0 remainder 72 |
| 2 | 102 ÷ 72 = 1 remainder 30 |
| 3 | 72 ÷ 30 = 2 remainder 12 |
| 4 | 30 ÷ 12 = 2 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 176 | 7920 |
| 40 and 122 | 2440 |
| 107 and 155 | 16585 |
| 110 and 198 | 990 |
| 169 and 84 | 14196 |