Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 380 and 382 the smallest integer that is 72580 that is divisible by both numbers.
Least Common Multiple (LCM) of 380 and 382 is 72580.
LCM(380,382) = 72580
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 380 and 382. First we will calculate the prime factors of 380 and 382.
Prime Factorization of 380
2 | 380 |
2 | 190 |
5 | 95 |
19 | 19 |
1 |
Prime factors of 380 are 2, 5,19. Prime factorization of 380 in exponential form is:
380 = 22×51×191
Prime Factorization of 382
2 | 382 |
191 | 191 |
1 |
Prime factors of 382 are 2,191. Prime factorization of 382 in exponential form is:
382 = 21×1911
Now multiplying the highest exponent prime factors to calculate the LCM of 380 and 382.
LCM(380,382) = 22×51×191×1911
LCM(380,382) = 72580
Factors of 380
List of positive integer factors of 380 that divides 380 without a remainder.
1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380
Factors of 382
List of positive integer factors of 382 that divides 382 without a remainder.
1, 2, 191, 382
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 380 and 382, than apply into the LCM equation.
GCF(380,382) = 2
LCM(380,382) = ( 380 × 382) / 2
LCM(380,382) = 145160 / 2
LCM(380,382) = 72580
(i) The LCM of 382 and 380 is associative
LCM of 380 and 382 = LCM of 382 and 380
1. What is the LCM of 380 and 382?
Answer: LCM of 380 and 382 is 72580.
2. What are the Factors of 380?
Answer: Factors of 380 are 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380. There are 12 integers that are factors of 380. The greatest factor of 380 is 380.
3. What are the Factors of 382?
Answer: Factors of 382 are 1, 2, 191, 382. There are 4 integers that are factors of 382. The greatest factor of 382 is 382.
4. How to Find the LCM of 380 and 382?
Answer:
Least Common Multiple of 380 and 382 = 72580
Step 1: Find the prime factorization of 380
380 = 2 x 2 x 5 x 19
Step 2: Find the prime factorization of 382
382 = 2 x 191
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 72580 = 2 x 2 x 5 x 19 x 191
Step 4: Therefore, the least common multiple of 380 and 382 is 72580.