Question 282015: NEED TO FIND LEAST COMMON MULTIPLE OF THE NUMBERS
105 AND 180
Answer by solver91311(24713)   (Show Source):
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The LCM is the smallest number that is a multiple of both given numbers.
Step 1: Find the prime factorization of each of your numbers:
105. Odd, 2 is not a factor. Sum of the digits is 6, 6 is divisible by 3, so 105 is divisible by 3 and equals 35.
35 is not divisible by 3.
35 ends in 5, so is divisible by 5 and equals 7
7 is prime
Then the prime factorization of 105 is 3 times 5 times 7
180. Even, divisible by 2 equals 90
90. Even, divisible by 2 equals 45
45. Divisible by 3, equals 15
15. Divisible by 3, equals 5
5 is prime
The prime factorization of 180 is 2 times 2 times 3 times 3 times 5
The factor 2 occurs most often in 180 and occurs 2 times, so the LCM needs 2 factors of 2
The factor 3 occurs most often in 180 and occurs 2 times, so the LCM needs 2 factors of 3.
The factor 5 occurs once in each number, so the LCM needs one factor of 5
The factor 7 occurs most often in 105 and occurs once, so the LCM needs one factor of 7
2 times 2 times 3 times 3 times 5 times 7 = 36 times 35 = 1260
John
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