LCM of 120, 210 and 225.
Answers
Answer:
The instructions to find the LCM of 120, 210 and 225 are the next:
1. Decompose all numbers into prime factors
120 2 60 2 30 2 15 3 5 5 1 210 2 105 3 35 5 7 7 1 225 3 75 3 25 5 5 5 1
2. Write all numbers as the product of its prime factors
Prime factors of 120 = 23 . 3 . 5
Prime factors of 210 = 2 . 3 . 5 . 7
Prime factors of 225 = 32 . 52
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, 52
Uncommon prime factors: 2 , 7
Uncommon prime factors with the greatest exponent: 23, 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. 52. 23. 71 = 1260
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Step-by-step explanation:
120=2×2×2×3×5=2^3×3×5
210=2×3×5×7
225=3×3×5×5=3^2×5^2
LCM= 2^3×3^2×5^2×7=8×9×25×7=12600