Least Common Multiple (LCM) of 60 and 119
The least common multiple (LCM) of 60 and 119 is 7140.
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 60 and 119?
First, calculate the GCD of 60 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 119 = 0 remainder 60 |
| 2 | 119 ÷ 60 = 1 remainder 59 |
| 3 | 60 ÷ 59 = 1 remainder 1 |
| 4 | 59 ÷ 1 = 59 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 108 | 3456 |
| 115 and 74 | 8510 |
| 176 and 147 | 25872 |
| 166 and 86 | 7138 |
| 16 and 88 | 176 |