Least Common Multiple of 1890 and 1896

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Free LCM Calculator determines the least common multiple (LCM) between 1890 and 1896 the smallest integer that is 597240 that is divisible by both numbers.

Least Common Multiple (LCM) of 1890 and 1896 is 597240.

LCM(1890,1896) = 597240

LCM of 1890 and 1896

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

LCM of:
and

Least Common Multiple of 1890 and 1896

LCM of 1890 and 1896 is 597240

Least common multiple can be found by multiplying the highest exponent prime factors of 1890 and 1896. First we will calculate the prime factors of 1890 and 1896.

Prime Factorization of 1890


2 1890
3 945
3 315
3 105
5 35
7 7
1

Prime factors of 1890 are 2, 3, 5,7. Prime factorization of 1890 in exponential form is:

1890 = 21×33×51×71

Prime Factorization of 1896


2 1896
2 948
2 474
3 237
79 79
1

Prime factors of 1896 are 2, 3,79. Prime factorization of 1896 in exponential form is:

1896 = 23×31×791

Now multiplying the highest exponent prime factors to calculate the LCM of 1890 and 1896.

LCM(1890,1896) = 23×33×51×71×791
LCM(1890,1896) = 597240

Factors of 1890

List of positive integer factors of 1890 that divides 1890 without a remainder.

1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945, 1890

Factors of 1896

List of positive integer factors of 1896 that divides 1896 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 79, 158, 237, 316, 474, 632, 948, 1896

Least Common Multiple of 1890 and 1896 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1890 and 1896, than apply into the LCM equation.

GCF(1890,1896) = 6
LCM(1890,1896) = ( 1890 × 1896) / 6
LCM(1890,1896) = 3583440 / 6
LCM(1890,1896) = 597240

Properties of LCM 1890 and 1896

(i) The LCM of 1896 and 1890 is associative

LCM of 1890 and 1896 = LCM of 1896 and 1890

Related Least Common Multiples of 1890

Related Least Common Multiples of 1896

Frequently Asked Questions on LCM of 1890 and 1896

1. What is the LCM of 1890 and 1896?

Answer: LCM of 1890 and 1896 is 597240.

2. What are the Factors of 1890?

Answer: Factors of 1890 are 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 27, 30, 35, 42, 45, 54, 63, 70, 90, 105, 126, 135, 189, 210, 270, 315, 378, 630, 945, 1890. There are 32 integers that are factors of 1890. The greatest factor of 1890 is 1890.

3. What are the Factors of 1896?

Answer: Factors of 1896 are 1, 2, 3, 4, 6, 8, 12, 24, 79, 158, 237, 316, 474, 632, 948, 1896. There are 16 integers that are factors of 1896. The greatest factor of 1896 is 1896.

4. How to Find the LCM of 1890 and 1896?

Answer:

Least Common Multiple of 1890 and 1896 = 597240

Step 1: Find the prime factorization of 1890

1890 = 2 x 3 x 3 x 3 x 5 x 7

Step 2: Find the prime factorization of 1896

1896 = 2 x 2 x 2 x 3 x 79

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 597240 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 7 x 79

Step 4: Therefore, the least common multiple of 1890 and 1896 is 597240.