Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 362 and 369 the smallest integer that is 133578 that is divisible by both numbers.
Least Common Multiple (LCM) of 362 and 369 is 133578.
LCM(362,369) = 133578
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 362 and 369. First we will calculate the prime factors of 362 and 369.
Prime Factorization of 362
2 | 362 |
181 | 181 |
1 |
Prime factors of 362 are 2,181. Prime factorization of 362 in exponential form is:
362 = 21×1811
Prime Factorization of 369
3 | 369 |
3 | 123 |
41 | 41 |
1 |
Prime factors of 369 are 3,41. Prime factorization of 369 in exponential form is:
369 = 32×411
Now multiplying the highest exponent prime factors to calculate the LCM of 362 and 369.
LCM(362,369) = 21×32×411×1811
LCM(362,369) = 133578
Factors of 362
List of positive integer factors of 362 that divides 362 without a remainder.
1, 2, 181, 362
Factors of 369
List of positive integer factors of 369 that divides 369 without a remainder.
1, 3, 9, 41, 123, 369
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 362 and 369, than apply into the LCM equation.
GCF(362,369) = 1
LCM(362,369) = ( 362 × 369) / 1
LCM(362,369) = 133578 / 1
LCM(362,369) = 133578
(i) The LCM of 369 and 362 is associative
LCM of 362 and 369 = LCM of 369 and 362
1. What is the LCM of 362 and 369?
Answer: LCM of 362 and 369 is 133578.
2. What are the Factors of 362?
Answer: Factors of 362 are 1, 2, 181, 362. There are 4 integers that are factors of 362. The greatest factor of 362 is 362.
3. What are the Factors of 369?
Answer: Factors of 369 are 1, 3, 9, 41, 123, 369. There are 6 integers that are factors of 369. The greatest factor of 369 is 369.
4. How to Find the LCM of 362 and 369?
Answer:
Least Common Multiple of 362 and 369 = 133578
Step 1: Find the prime factorization of 362
362 = 2 x 181
Step 2: Find the prime factorization of 369
369 = 3 x 3 x 41
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 133578 = 2 x 3 x 3 x 41 x 181
Step 4: Therefore, the least common multiple of 362 and 369 is 133578.