Least Common Multiple (LCM) of 121 and 178
The least common multiple (LCM) of 121 and 178 is 21538.
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 178?
First, calculate the GCD of 121 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 178 = 0 remainder 121 |
| 2 | 178 ÷ 121 = 1 remainder 57 |
| 3 | 121 ÷ 57 = 2 remainder 7 |
| 4 | 57 ÷ 7 = 8 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 86 | 602 |
| 109 and 88 | 9592 |
| 141 and 50 | 7050 |
| 188 and 84 | 3948 |
| 164 and 130 | 10660 |