Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 1929 and 1932 the smallest integer that is 1242276 that is divisible by both numbers.
Least Common Multiple (LCM) of 1929 and 1932 is 1242276.
LCM(1929,1932) = 1242276
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 1929 and 1932. First we will calculate the prime factors of 1929 and 1932.
Prime Factorization of 1929
3 | 1929 |
643 | 643 |
1 |
Prime factors of 1929 are 3,643. Prime factorization of 1929 in exponential form is:
1929 = 31×6431
Prime Factorization of 1932
2 | 1932 |
2 | 966 |
3 | 483 |
7 | 161 |
23 | 23 |
1 |
Prime factors of 1932 are 2, 3, 7,23. Prime factorization of 1932 in exponential form is:
1932 = 22×31×71×231
Now multiplying the highest exponent prime factors to calculate the LCM of 1929 and 1932.
LCM(1929,1932) = 22×31×71×231×6431
LCM(1929,1932) = 1242276
Factors of 1929
List of positive integer factors of 1929 that divides 1929 without a remainder.
1, 3, 643, 1929
Factors of 1932
List of positive integer factors of 1932 that divides 1932 without a remainder.
1, 2, 3, 4, 6, 7, 12, 14, 21, 23, 28, 42, 46, 69, 84, 92, 138, 161, 276, 322, 483, 644, 966, 1932
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1929 and 1932, than apply into the LCM equation.
GCF(1929,1932) = 3
LCM(1929,1932) = ( 1929 × 1932) / 3
LCM(1929,1932) = 3726828 / 3
LCM(1929,1932) = 1242276
(i) The LCM of 1932 and 1929 is associative
LCM of 1929 and 1932 = LCM of 1932 and 1929
1. What is the LCM of 1929 and 1932?
Answer: LCM of 1929 and 1932 is 1242276.
2. What are the Factors of 1929?
Answer: Factors of 1929 are 1, 3, 643, 1929. There are 4 integers that are factors of 1929. The greatest factor of 1929 is 1929.
3. What are the Factors of 1932?
Answer: Factors of 1932 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 23, 28, 42, 46, 69, 84, 92, 138, 161, 276, 322, 483, 644, 966, 1932. There are 24 integers that are factors of 1932. The greatest factor of 1932 is 1932.
4. How to Find the LCM of 1929 and 1932?
Answer:
Least Common Multiple of 1929 and 1932 = 1242276
Step 1: Find the prime factorization of 1929
1929 = 3 x 643
Step 2: Find the prime factorization of 1932
1932 = 2 x 2 x 3 x 7 x 23
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 1242276 = 2 x 2 x 3 x 7 x 23 x 643
Step 4: Therefore, the least common multiple of 1929 and 1932 is 1242276.