Least Common Multiple (LCM) of 121 and 72
The least common multiple (LCM) of 121 and 72 is 8712.
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 121 and 72?
First, calculate the GCD of 121 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 72 = 1 remainder 49 |
| 2 | 72 ÷ 49 = 1 remainder 23 |
| 3 | 49 ÷ 23 = 2 remainder 3 |
| 4 | 23 ÷ 3 = 7 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 13 | 2457 |
| 10 and 157 | 1570 |
| 121 and 117 | 14157 |
| 134 and 195 | 26130 |
| 117 and 68 | 7956 |