Least Common Multiple (LCM) of 61 and 119
The least common multiple (LCM) of 61 and 119 is 7259.
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 61 and 119?
First, calculate the GCD of 61 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 119 = 0 remainder 61 |
| 2 | 119 ÷ 61 = 1 remainder 58 |
| 3 | 61 ÷ 58 = 1 remainder 3 |
| 4 | 58 ÷ 3 = 19 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 154 | 13706 |
| 14 and 95 | 1330 |
| 117 and 74 | 8658 |
| 162 and 145 | 23490 |
| 188 and 44 | 2068 |