Find the mCF of 30,60,90 and 105
Answers
1. Decompose all numbers into prime factors
30 2 15 3 5 5 1 60 2 30 2 15 3 5 5 1 90 2 45 3 15 3 5 5 1 105 3 35 5 7 7 1
2. Write all numbers as the product of its prime factors
Prime factors of 30 = 2 . 3 . 5
Prime factors of 60 = 22 . 3 . 5
Prime factors of 90 = 2 . 32 . 5
Prime factors of 105 = 3 . 5 . 7
3. Choose the common and uncommon prime factors with the greatest exponent
Common prime factors: 3 , 5
Common prime factors with the greatest exponent: 32, 51
Uncommon prime factors: 2 , 7
Uncommon prime factors with the greatest exponent: 22, 71
4. Calculate the Least Common Multiple or LCM
Remember, to find the LCM of several numbers you must multiply the common and uncommon prime factors with the greatest exponent of those numbers.
LCM = 32. 51. 22. 71 = 1260