Find the LCM of 12, 45,75 explanation
Answers
Calculate the Least Common Multiple or LCM of 12, 45 and 75
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The instructions to find the LCM of 12, 45 and 75 are the next:
1. Decompose all numbers into prime factors
12 =2 ,6 ,2 ,3 ,3 ,1
45 =3 ,15 ,3 ,5 ,5 ,1
75 =3 ,2,5 ,5 ,5 ,5 ,1
2. Write all numbers as the product of its prime factors
Prime factors of 12 = 22 . 3
Prime factors of 45 = 32 . 5
Prime factors of 75 = 3 . 52
3. Choose the common and uncommon prime factors with the greatest exponent
Common prime factors: 3
Common prime factors with the greatest exponent: 32
Uncommon prime factors: 2 , 5
Uncommon prime factors with the greatest exponent: 22, 52
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. 22. 52 = 900
Answer:
Here is the answer =>
Step-by-step explanation:
12=2*2*3
=2^2*3
45=3*3*5
=3^2*5
75=5*5*3
=5^2*3
As LCM is the product of the highest power of each factor.
So LCM(12,45,75)=2*2*3*3*5*5
=2^2*3^2*5^2
=4*9*25
=36*25
=900.
So the LCM of 12,45 and 75 is 900 which is the required answer.
HOPE IT HELPS.