Least Common Multiple (LCM) of 46 and 13
The least common multiple (LCM) of 46 and 13 is 598.
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 13?
First, calculate the GCD of 46 and 13 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 13 = 3 remainder 7 |
| 2 | 13 ÷ 7 = 1 remainder 6 |
| 3 | 7 ÷ 6 = 1 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 169 | 21801 |
| 28 and 141 | 3948 |
| 79 and 182 | 14378 |
| 157 and 42 | 6594 |
| 110 and 194 | 10670 |