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The LCM of 2³ * 3² * 5, 2² * 3³ * 7, and 2⁴ * 3 * 5² is:
24×33×52×7
23×32×5×7
24×33×5×7
22×32×5×7
24×33×52×7
To find the LCM, scan all prime bases (2, 3, 5, 7) and immediately pick the highest exponent assigned to each, ignoring the others entirely.
Three numbers expressed in their prime factorized forms: 23imes32imes51, 22imes33imes71, and 24imes31imes52.
LCM=∏Highest power of each prime factor present in the expressions
To find the LCM, scan all prime bases (2, 3, 5, 7) and immediately pick the highest exponent assigned to each, ignoring the others entirely.
Students often multiply all numbers present instead of choosing the maximum exponent for each prime factor, or forget to include primes that appear in only one number (like 7).
Identify unique prime factors
List all distinct prime factors present across the three numbers: these are 2, 3, 5, and 7.
2,3,5,7
Find the highest power for each prime
Compare the exponents for each prime base: For 2, max is 4. For 3, max is 3. For 5, max is 2. For 7, max is 1.
24,33,52,71
Calculate the LCM
Multiply these highest powers together to get the LCM: 24imes33imes52imes71.
24imes33imes52imes7
A is correct because the LCM is determined by the product of the highest power of every prime factor occurring in the given numbers, resulting in 24imes33imes52imes7.
This concept is foundational for solving HCF and LCM problems involving algebraic expressions and polynomials in subsequent topics like Algebra.
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