Find tha LCM by prime factorisation method 28 and 35 next digit 18,30 and 48
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Answer:
59220 is the LCM by prime factorisation method
Answer:
The Least Common Multiple (LCM) is also referred to as the Lowest Common Multiple (LCM) and Least Common Divisor (LCD). For two integers a and b, denoted LCM(a,b), the LCM is the smallest positive integer that is evenly divisible by both a and b. For example, LCM(2,3) = 6 and LCM(6,10) = 30.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
Multiples of 7: 7, 14, 21, 28, 35, 42, 56, 63
Multiples of 21: 21, 42, 63
Find the smallest number that is on all of the lists. We have it in bold above.
So LCM(6, 7, 21) is 42
How to find LCM by Prime Factorization
Find all the prime factors of each given number.
List all the prime numbers found, as many times as they occur most often for any one given number.
Multiply the list of prime factors together to find the LCM.
The LCM(a,b) is calculated by finding the prime factorization of both a and b. Use the same process for the LCM of more than 2 numbers.
For example, for LCM(12,30) we find:
Prime factorization of 12 = 2 × 2 × 3
Prime factorization of 30 = 2 × 3 × 5
Using all prime numbers found as often as each occurs most often we take 2 × 2 × 3 × 5 = 60
Therefore LCM(12,30) = 60.
Prime factors of 12 = 2 × 2 × 3 = 22 × 31
Prime factors of 18 = 2 × 3 × 3 = 21 × 32
Prime factors of 30 = 2 × 3 × 5 = 21 × 31 × 51
List all the prime numbers found, as many times as they occur most often for any one given number and multiply them together to find the LCM
2 × 2 × 3 × 3 × 5 = 180
Using exponents instead, multiply together each of the prime numbers with the highest power
22 × 32 × 51 = 180
So LCM(12,18,30) = 180
Example: LCM(24,300)
Prime factors of 24 = 2 × 2 × 2 × 3 = 23 × 31
Prime factors of 300 = 2 × 2 × 3 × 5 × 5 = 22 × 31 × 52
List all the prime numbers found, as many times as they occur most often for any one given number and multiply them together to find the LCM
2 × 2 × 2 × 3 × 5 × 5 = 600
Using exponents instead, multiply together each of the prime numbers with the highest power
23 × 31 × 52 = 600
So LCM(24,300) = 600
How to Find LCM Using the Cake Method (Ladder Method)
The cake method uses division to find the LCM of a set of numbers. People use the cake or ladder method as the fastest and easiest way to find the LCM because it is simple division.
The cake method is the same as the ladder method, the box method, the factor box method and the grid method of shortcuts to find the LCM. The boxes and grids might look a little different, but they all use division by primes to find LCM.
Find the LCM(10, 12, 15, 75)
Write down your numbers in a cake layer (row)
Cake / Ladder
10 12 15 75
Divide the layer numbers by a prime number that is evenly divisible into two or more numbers in the layer and bring down the result into the next layer.
Cake / Ladder
2 10 12 15 75
5 6
If any number in the layer is not evenly divisible just bring down that number.
Cake / Ladder
2 10 12 15 75
5 6 15 75
Continue dividing cake layers by prime numbers.
When there are no more primes that evenly divided into two or more numbers you are done.
Cake / Ladder
2 10 12 15 75
3 5 6 15 75
5 5 2 5 25
1 2 1 5
The LCM is the product of the numbers in the L shape, left column and bottom row. 1 is ignored.
LCM = 2 × 3 × 5 × 2 × 5
LCM = 300
Therefore, LCM(10, 12, 15, 75) = 300
Step-by-step explanation: