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Answer To find the smallest number that is divisible by both 90 and 144 when increased by 20, we need to find the least common multiple (LCM) of 90 and 144. Then, we'll add 20 to that LCM to get our answer.
First, let's find the LCM of 90 and 144.
The prime factorization of 90 is 2×32×52×32×5.
The prime factorization of 144 is 24×3224×32.
To find the LCM, we take the highest power of each prime factor that appears in either number:
LCM=24×32×5=720LCM=24×32×5=720
Now, we add 20 to 720:
720+20=740720+20=740
So, the smallest number that, when increased by 20, is exactly divisible by both 90 and 144 is 740.
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