Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1238 and 1240 the smallest integer that is 767560 that is divisible by both numbers.
Least Common Multiple (LCM) of 1238 and 1240 is 767560.
LCM(1238,1240) = 767560
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 1238 and 1240. First we will calculate the prime factors of 1238 and 1240.
Prime Factorization of 1238
2 | 1238 |
619 | 619 |
1 |
Prime factors of 1238 are 2,619. Prime factorization of 1238 in exponential form is:
1238 = 21×6191
Prime Factorization of 1240
2 | 1240 |
2 | 620 |
2 | 310 |
5 | 155 |
31 | 31 |
1 |
Prime factors of 1240 are 2, 5,31. Prime factorization of 1240 in exponential form is:
1240 = 23×51×311
Now multiplying the highest exponent prime factors to calculate the LCM of 1238 and 1240.
LCM(1238,1240) = 23×51×311×6191
LCM(1238,1240) = 767560
Factors of 1238
List of positive integer factors of 1238 that divides 1238 without a remainder.
1, 2, 619, 1238
Factors of 1240
List of positive integer factors of 1240 that divides 1240 without a remainder.
1, 2, 4, 5, 8, 10, 20, 31, 40, 62, 124, 155, 248, 310, 620, 1240
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1238 and 1240, than apply into the LCM equation.
GCF(1238,1240) = 2
LCM(1238,1240) = ( 1238 × 1240) / 2
LCM(1238,1240) = 1535120 / 2
LCM(1238,1240) = 767560
(i) The LCM of 1240 and 1238 is associative
LCM of 1238 and 1240 = LCM of 1240 and 1238
1. What is the LCM of 1238 and 1240?
Answer: LCM of 1238 and 1240 is 767560.
2. What are the Factors of 1238?
Answer: Factors of 1238 are 1, 2, 619, 1238. There are 4 integers that are factors of 1238. The greatest factor of 1238 is 1238.
3. What are the Factors of 1240?
Answer: Factors of 1240 are 1, 2, 4, 5, 8, 10, 20, 31, 40, 62, 124, 155, 248, 310, 620, 1240. There are 16 integers that are factors of 1240. The greatest factor of 1240 is 1240.
4. How to Find the LCM of 1238 and 1240?
Answer:
Least Common Multiple of 1238 and 1240 = 767560
Step 1: Find the prime factorization of 1238
1238 = 2 x 619
Step 2: Find the prime factorization of 1240
1240 = 2 x 2 x 2 x 5 x 31
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 767560 = 2 x 2 x 2 x 5 x 31 x 619
Step 4: Therefore, the least common multiple of 1238 and 1240 is 767560.