lcm 4,8

{ "query": { "display": "lcm $$4,\\:8$$", "symbolab_question": "PRE_ALGEBRA#lcm 4,8" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Factors & Primes", "subTopic": "LCM", "default": "8", "meta": { "showVerify": true } }, "methods": [ { "method": "Solve using prime factors", "query": { "display": "lcm by prime factors $$4,\\:8$$", "symbolab_question": "lcmfact 4,8" } }, { "method": "Solve using multipliers", "query": { "display": "lcm by multipliers $$4,\\:8$$", "symbolab_question": "lcmmult 4,8" } }, { "method": "Solve using GCD", "query": { "display": "lcm by gcd $$4,\\:8$$", "symbolab_question": "lcmgcd 4,8" } } ], "steps": { "type": "interim", "title": "Least Common Multiplier of $$4,\\:8:{\\quad}8$$", "input": "4,\\:8", "steps": [ { "type": "definition", "title": "Least Common Multiplier (LCM)", "text": "The LCM of $$a,\\:b$$ is the smallest positive number that is divisible by both $$a$$ and $$b$$" }, { "type": "interim", "title": "Prime factorization of $$4:{\\quad}2\\cdot\\:2$$", "input": "4", "steps": [ { "type": "step", "primary": "$$4\\:$$divides by $$2\\quad\\:4=2\\cdot\\:2$$", "result": "=2\\cdot\\:2" } ], "meta": { "solvingClass": "Composite Integer", "interimType": "Prime Fac 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRsG/uC0ndYtZpJL4uAxK7FI/y9DKGIPglJ+qMi9xDu2KE1OovxZAaXg7BtrFPk4UcCzRnGgMN6CYRfod7Mq0dp39fF/zAtU5baHQ1hwgXA+n" } }, { "type": "interim", "title": "Prime factorization of $$8:{\\quad}2\\cdot\\:2\\cdot\\:2$$", "input": "8", "steps": [ { "type": "step", "primary": "$$8\\:$$divides by $$2\\quad\\:8=4\\cdot\\:2$$", "result": "=2\\cdot\\:4" }, { "type": "step", "primary": "$$4\\:$$divides by $$2\\quad\\:4=2\\cdot\\:2$$", "result": "=2\\cdot\\:2\\cdot\\:2" } ], "meta": { "solvingClass": "Composite Integer", "interimType": "Prime Fac 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xyoU2cWyPLDgE1QLLHeauuc3PHQdChPJ2JhfqHT+ZU0OMrfn8NOj0LUzuzje6xTyxRtXnBik8vDPXVw+nKWp28DI/y9DKGIPglJ+qMi9xDu2KE1OovxZAaXg7BtrFPk4UcCzRnGgMN6CYRfod7Mq0dp1RcgsS082tQWmOBW6FvhEw" } }, { "type": "step", "primary": "Multiply each factor the greatest number of times it occurs in either $$4$$ or $$8$$", "result": "=2\\cdot\\:2\\cdot\\:2" }, { "type": "step", "primary": "Multiply the numbers: $$2\\cdot\\:2\\cdot\\:2=8$$", "result": "=8" } ], "meta": { "solvingClass": "LCM" } }, "meta": { "showVerify": true } }