Least Common Multiple (LCM) of 113 and 46
The least common multiple (LCM) of 113 and 46 is 5198.
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 113 and 46?
First, calculate the GCD of 113 and 46 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 46 = 2 remainder 21 |
| 2 | 46 ÷ 21 = 2 remainder 4 |
| 3 | 21 ÷ 4 = 5 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 179 and 157 | 28103 |
| 102 and 87 | 2958 |
| 156 and 160 | 6240 |
| 178 and 36 | 3204 |
| 138 and 101 | 13938 |