Least Common Multiple (LCM) of 101 and 72
The least common multiple (LCM) of 101 and 72 is 7272.
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 101 and 72?
First, calculate the GCD of 101 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 72 = 1 remainder 29 |
| 2 | 72 ÷ 29 = 2 remainder 14 |
| 3 | 29 ÷ 14 = 2 remainder 1 |
| 4 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 16 | 1232 |
| 118 and 46 | 2714 |
| 135 and 61 | 8235 |
| 180 and 157 | 28260 |
| 149 and 54 | 8046 |