Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 46 and 39 the smallest integer that is 1794 that is divisible by both numbers.
Least Common Multiple (LCM) of 46 and 39 is 1794.
LCM(46,39) = 1794
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 46 and 39. First we will calculate the prime factors of 46 and 39.
Prime Factorization of 46
2 | 46 |
23 | 23 |
1 |
Prime factors of 46 are 2,23. Prime factorization of 46 in exponential form is:
46 = 21×231
Prime Factorization of 39
3 | 39 |
13 | 13 |
1 |
Prime factors of 39 are 3,13. Prime factorization of 39 in exponential form is:
39 = 31×131
Now multiplying the highest exponent prime factors to calculate the LCM of 46 and 39.
LCM(46,39) = 21×31×131×231
LCM(46,39) = 1794
Factors of 46
List of positive integer factors of 46 that divides 46 without a remainder.
1, 2, 23, 46
Factors of 39
List of positive integer factors of 39 that divides 39 without a remainder.
1, 3, 13, 39
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 46 and 39, than apply into the LCM equation.
GCF(46,39) = 1
LCM(46,39) = ( 46 × 39) / 1
LCM(46,39) = 1794 / 1
LCM(46,39) = 1794
(i) The LCM of 39 and 46 is associative
LCM of 46 and 39 = LCM of 39 and 46
1. What is the LCM of 46 and 39?
Answer: LCM of 46 and 39 is 1794.
2. What are the Factors of 46?
Answer: Factors of 46 are 1, 2, 23, 46. There are 4 integers that are factors of 46. The greatest factor of 46 is 46.
3. What are the Factors of 39?
Answer: Factors of 39 are 1, 3, 13, 39. There are 4 integers that are factors of 39. The greatest factor of 39 is 39.
4. How to Find the LCM of 46 and 39?
Answer:
Least Common Multiple of 46 and 39 = 1794
Step 1: Find the prime factorization of 46
46 = 2 x 23
Step 2: Find the prime factorization of 39
39 = 3 x 13
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1794 = 2 x 3 x 13 x 23
Step 4: Therefore, the least common multiple of 46 and 39 is 1794.