Question

lcm by prime factorization question 80 90 120​

Answer 1

1. Decompose all numbers into prime factors
80 2 40 2 20 2 10 2 5 5 1 90 2 45 3 15 3 5 5 1
120 2 60 2 30 2 15 3 5 5 1 126 2 63 3 21 3 7 7 1
2. Write all numbers as the product of its prime factors
Prime factors of 80 = 24 . 5
Prime factors of 90 = 2 . 32 . 5
Prime factors of 120 = 23 . 3 . 5
Prime factors of 126 = 2 . 32 . 7
3. Choose the common and uncommon prime factors with the greatest exponent
Common prime factors: 2
Common prime factors with the greatest exponent: 24
Uncommon prime factors: 5 , 3 , 7
Uncommon prime factors with the greatest exponent: 51, 32, 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 = 24. 51. 32. 71 = 5040

Answer 2

Step-by-step explanation:

80= 2×2×2×2×5

90=2×5×3×3

120=2×2×2×5×3

LCM=2⁴×5×3²=720