Least Common Multiple (LCM) of 70 and 111
The least common multiple (LCM) of 70 and 111 is 7770.
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 70 and 111?
First, calculate the GCD of 70 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 70 ÷ 111 = 0 remainder 70 |
| 2 | 111 ÷ 70 = 1 remainder 41 |
| 3 | 70 ÷ 41 = 1 remainder 29 |
| 4 | 41 ÷ 29 = 1 remainder 12 |
| 5 | 29 ÷ 12 = 2 remainder 5 |
| 6 | 12 ÷ 5 = 2 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 193 | 4825 |
| 60 and 134 | 4020 |
| 39 and 137 | 5343 |
| 77 and 91 | 1001 |
| 134 and 69 | 9246 |