I don not understand how to do least common mutiples.
Can I please get some help.
I need to find the least common multiple of 420 and 196.
there is a real neat way to do this which works for the LCM of any number of numerals.
420 196
-------| divide each number by a common factor
105 49 | 4
15...7.} 7
there are no more common factors
so the LCM is the multiplation of the numbers on the far right as well as the last row
so LCM = 4 x 7 x 15 x 7 2940
if you had more than 3 numbers to start with there was a common factor for only some of them, take it out until there is no common factor for any
e.g.
400 250 230
200 125 215 | 2
40..25 43...| 5
8....5 43...| 5
so LCM = 2x5x5x8x5x43
43
To find the least common multiple (LCM) of two numbers, you can use the method called "finding prime factors." Here's how you can apply this method to find the LCM of 420 and 196:
Step 1: Write down the prime factorization of each number.
420 = 2^2 x 3 x 5 x 7
196 = 2^2 x 7^2
Step 2: Identify all the unique prime factors from both numbers. They are 2, 3, 5, and 7.
Step 3: Determine the maximum exponent for each prime factor.
For 2, the maximum exponent is 2.
For 3, the maximum exponent is 1.
For 5, the maximum exponent is 1.
For 7, the maximum exponent is 2.
Step 4: Multiply the prime factors with their maximum exponents to find the LCM.
LCM = 2^2 x 3^1 x 5^1 x 7^2
= 4 x 3 x 5 x 49
= 2940
Therefore, the LCM of 420 and 196 is 2940.
The same method can be applied to find the LCM of any number of numerals. Simply find the prime factorization of each number, identify the unique prime factors, determine the maximum exponent for each prime factor, and then multiply them together to get the LCM.