Least Common Multiple (LCM) of 113 and 62
The least common multiple (LCM) of 113 and 62 is 7006.
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 62?
First, calculate the GCD of 113 and 62 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 62 = 1 remainder 51 |
| 2 | 62 ÷ 51 = 1 remainder 11 |
| 3 | 51 ÷ 11 = 4 remainder 7 |
| 4 | 11 ÷ 7 = 1 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 59 | 708 |
| 157 and 70 | 10990 |
| 30 and 24 | 120 |
| 180 and 145 | 5220 |
| 13 and 142 | 1846 |