Least Common Multiple (LCM) of 194 and 121
The least common multiple (LCM) of 194 and 121 is 23474.
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 194 and 121?
First, calculate the GCD of 194 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 121 = 1 remainder 73 |
| 2 | 121 ÷ 73 = 1 remainder 48 |
| 3 | 73 ÷ 48 = 1 remainder 25 |
| 4 | 48 ÷ 25 = 1 remainder 23 |
| 5 | 25 ÷ 23 = 1 remainder 2 |
| 6 | 23 ÷ 2 = 11 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 112 | 112 |
| 115 and 160 | 3680 |
| 32 and 155 | 4960 |
| 124 and 126 | 7812 |
| 140 and 12 | 420 |