Least Common Multiple (LCM) of 174 and 121
The least common multiple (LCM) of 174 and 121 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 174 and 121?
First, calculate the GCD of 174 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 121 = 1 remainder 53 |
| 2 | 121 ÷ 53 = 2 remainder 15 |
| 3 | 53 ÷ 15 = 3 remainder 8 |
| 4 | 15 ÷ 8 = 1 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 118 | 5310 |
| 100 and 140 | 700 |
| 182 and 179 | 32578 |
| 135 and 50 | 1350 |
| 136 and 145 | 19720 |