Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1997 and 2002 the smallest integer that is 3997994 that is divisible by both numbers.
Least Common Multiple (LCM) of 1997 and 2002 is 3997994.
LCM(1997,2002) = 3997994
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 1997 and 2002. First we will calculate the prime factors of 1997 and 2002.
Prime Factorization of 1997
1997 | 1997 |
1 |
Prime factors of 1997 are 1997. Prime factorization of 1997 in exponential form is:
1997 = 19971
Prime Factorization of 2002
2 | 2002 |
7 | 1001 |
11 | 143 |
13 | 13 |
1 |
Prime factors of 2002 are 2, 7, 11,13. Prime factorization of 2002 in exponential form is:
2002 = 21×71×111×131
Now multiplying the highest exponent prime factors to calculate the LCM of 1997 and 2002.
LCM(1997,2002) = 21×71×111×131×19971
LCM(1997,2002) = 3997994
Factors of 1997
List of positive integer factors of 1997 that divides 1997 without a remainder.
1, 1997
Factors of 2002
List of positive integer factors of 2002 that divides 2002 without a remainder.
1, 2, 7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286, 1001, 2002
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1997 and 2002, than apply into the LCM equation.
GCF(1997,2002) = 1
LCM(1997,2002) = ( 1997 × 2002) / 1
LCM(1997,2002) = 3997994 / 1
LCM(1997,2002) = 3997994
(i) The LCM of 2002 and 1997 is associative
LCM of 1997 and 2002 = LCM of 2002 and 1997
1. What is the LCM of 1997 and 2002?
Answer: LCM of 1997 and 2002 is 3997994.
2. What are the Factors of 1997?
Answer: Factors of 1997 are 1, 1997. There are 2 integers that are factors of 1997. The greatest factor of 1997 is 1997.
3. What are the Factors of 2002?
Answer: Factors of 2002 are 1, 2, 7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286, 1001, 2002. There are 16 integers that are factors of 2002. The greatest factor of 2002 is 2002.
4. How to Find the LCM of 1997 and 2002?
Answer:
Least Common Multiple of 1997 and 2002 = 3997994
Step 1: Find the prime factorization of 1997
1997 = 1997
Step 2: Find the prime factorization of 2002
2002 = 2 x 7 x 11 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 = 3997994 = 2 x 7 x 11 x 13 x 1997
Step 4: Therefore, the least common multiple of 1997 and 2002 is 3997994.