Find the LCM and pe HCF of the Following
1) 396, 720, 1080.
2) 1440, 1920, 1800.
Answers
what is LCM and HCF?
The full form of LCM is Lowest Common Multiple.It is the smallest positive integer that is evenly divisible by both the digits that are given.
The full form is Highest Common Factor. It found by finding all common factors of two numbers and selecting the largest one.
HCF of 396, 720, 1080.
The factors of 396 are: 1, 2, 3, 4, 6, 9, 11, 12, 18, 22, 33, 36, 44, 66, 99, 132, 198, 396
The factors of 720 are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, 720
The factors of 1080 are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540, 1080
Then the greatest common factor is 36.
HCF of 1440, 1920, 1800
The factors of 1440 are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 72, 80, 90, 96, 120, 144, 160, 180, 240, 288, 360, 480, 720, 1440
The factors of 1800 are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 25, 30, 36, 40, 45, 50, 60, 72, 75, 90, 100, 120, 150, 180, 200, 225, 300, 360, 450, 600, 900, 1800
The factors of 1920 are: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 128, 160, 192, 240, 320, 384, 480, 640, 960, 1920
Then the greatest common factor is 120.
How to find HCF
HCF can be calculated using:
- Factoring
- Prime factorization
LCF of 396, 720, 1080
List all prime factors for each number.
Prime Factorization of 396 is:
2 x 2 x 3 x 3 x 11 => 22 x 32 x 111
Prime Factorization of 720 is:
2 x 2 x 2 x 2 x 3 x 3 x 5 => 24 x 32 x 51
Prime Factorization of 1080 is:
2 x 2 x 2 x 3 x 3 x 3 x 5 => 23 x 33 x 51
For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
The new superset list is
2, 2, 2, 2, 3, 3, 3, 5, 11
Multiply these factors together to find the LCM.
LCM = 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 11 = 23760
LCF of 1440, 1920, 1800
How to find LCF
Besides using common factor calculator for least common multiples, LCM can be calculated using several methods.
Prime Factorization
Prime Factorization
List of multiples
Brute-Force method
Division Method