Answer:
2³×3⁵×5¹×7²
Step-by-step explanation:
In your example, Let's denote the two expressions as A and B where A = 2³×3⁴×7 and B = 2³×3⁵×5×7². Let further the number C be the LCM(A, B), then C denotes the smallest number that is divisible by both A and B. Since A and B are written as multiples of their prime factors you simply find for each prime factor their highest common exponent.
The Least Common Multiple C has two requirements, it must be a common multiple (be divisible by both A and B with an integer quotient, and it must the smallest such number. The first condition (being a common multiple) has been shown already so it remains to show that it is the smallest such number. By looking at the prime factorizations you can note that any smaller number C would cause either quotient C/A or C/B to have a non-integer value.
