Least Common Multiple (LCM) of 122 and 169
The least common multiple (LCM) of 122 and 169 is 20618.
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 122 and 169?
First, calculate the GCD of 122 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 169 = 0 remainder 122 |
| 2 | 169 ÷ 122 = 1 remainder 47 |
| 3 | 122 ÷ 47 = 2 remainder 28 |
| 4 | 47 ÷ 28 = 1 remainder 19 |
| 5 | 28 ÷ 19 = 1 remainder 9 |
| 6 | 19 ÷ 9 = 2 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 19 | 2014 |
| 119 and 30 | 3570 |
| 31 and 147 | 4557 |
| 170 and 11 | 1870 |
| 152 and 79 | 12008 |