Least Common Multiple (LCM) of 121 and 174
The least common multiple (LCM) of 121 and 174 is 21054.
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 174?
First, calculate the GCD of 121 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 174 = 0 remainder 121 |
| 2 | 174 ÷ 121 = 1 remainder 53 |
| 3 | 121 ÷ 53 = 2 remainder 15 |
| 4 | 53 ÷ 15 = 3 remainder 8 |
| 5 | 15 ÷ 8 = 1 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 192 | 8256 |
| 74 and 89 | 6586 |
| 31 and 13 | 403 |
| 136 and 14 | 952 |
| 91 and 132 | 12012 |