Least Common Multiple (LCM) of 46 and 169
The least common multiple (LCM) of 46 and 169 is 7774.
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 46 and 169?
First, calculate the GCD of 46 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 169 = 0 remainder 46 |
| 2 | 169 ÷ 46 = 3 remainder 31 |
| 3 | 46 ÷ 31 = 1 remainder 15 |
| 4 | 31 ÷ 15 = 2 remainder 1 |
| 5 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 113 | 13899 |
| 39 and 81 | 1053 |
| 109 and 66 | 7194 |
| 111 and 46 | 5106 |
| 191 and 106 | 20246 |