Least Common Multiple (LCM) of 107 and 72
The least common multiple (LCM) of 107 and 72 is 7704.
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 107 and 72?
First, calculate the GCD of 107 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 72 = 1 remainder 35 |
| 2 | 72 ÷ 35 = 2 remainder 2 |
| 3 | 35 ÷ 2 = 17 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 148 | 24716 |
| 151 and 71 | 10721 |
| 14 and 158 | 1106 |
| 184 and 110 | 10120 |
| 129 and 176 | 22704 |