Least Common Multiple (LCM) of 121 and 169
The least common multiple (LCM) of 121 and 169 is 20449.
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 169?
First, calculate the GCD of 121 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 121 ÷ 169 = 0 remainder 121 |
| 2 | 169 ÷ 121 = 1 remainder 48 |
| 3 | 121 ÷ 48 = 2 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 |
|---|---|
| 12 and 114 | 228 |
| 192 and 97 | 18624 |
| 130 and 108 | 7020 |
| 14 and 120 | 840 |
| 88 and 146 | 6424 |