Least Common Multiple (LCM) of 103 and 72
The least common multiple (LCM) of 103 and 72 is 7416.
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 103 and 72?
First, calculate the GCD of 103 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 72 = 1 remainder 31 |
| 2 | 72 ÷ 31 = 2 remainder 10 |
| 3 | 31 ÷ 10 = 3 remainder 1 |
| 4 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 164 | 17548 |
| 103 and 141 | 14523 |
| 136 and 145 | 19720 |
| 160 and 18 | 1440 |
| 136 and 195 | 26520 |