Least Common Multiple (LCM) of 111 and 70
The least common multiple (LCM) of 111 and 70 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 111 and 70?
First, calculate the GCD of 111 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 70 = 1 remainder 41 |
| 2 | 70 ÷ 41 = 1 remainder 29 |
| 3 | 41 ÷ 29 = 1 remainder 12 |
| 4 | 29 ÷ 12 = 2 remainder 5 |
| 5 | 12 ÷ 5 = 2 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 88 | 13112 |
| 17 and 74 | 1258 |
| 37 and 162 | 5994 |
| 80 and 146 | 5840 |
| 135 and 117 | 1755 |